Log Calculator Or Logarithmic Calculator Online

The logarithm, or log, is the inverse of the mathematical operation of exponentiation. This means that the log of a number is the number that a fixed base has to be raised to in order to yield the number. Conventionally, log implies that base 10 is being used, though the base can technically be anything. When the base is e, ln is usually written, rather than log_e. log₂, the binary logarithm, is another base that is typically used with logarithms. If for example:

x = b^y; then y = log_bx; where b is the base

Each of the mentioned bases are typically used in different applications. Base 10 is commonly used in science and engineering, base e in math and physics, and base 2 in computer science.

Basic Log Rules:

When the argument of a logarithm is the product of two numerals, the logarithm can be re-written as the addition of the logarithm of each of the numerals.

log_b(x × y) = log_bx + log_by
EX: log(1 × 10) = log(1) + log(10) = 0 + 1 = 1

When the argument of a logarithm is a fraction, the logarithm can be re-written as the subtraction of the logarithm of the numerator minus the logarithm of the denominator.

log_b(x / y) = log_bx - log_by
EX: log(10 / 2) = log(10) - log(2) = 1 - 0.301 = 0.699

If there is an exponent in the argument of a logarithm, the exponent can be pulled out of the logarithm and multiplied.

log_bx^y = y × log_bx
EX: log(2⁶) = 6 × log(2) = 1.806

It is also possible to change the base of the logarithm using the following rule.

logb(x) =

logk(x) logk(b)

EX: log10(x) =

log2(x) log2(10)

To switch the base and argument, use the following rule.

logb(c) =

1 logc(b)

EX:   log5(2) =

1 log2(5)

Other common logarithms to take note of include:

log_b(1) = 0
log_b(b) = 1
log_b(0) = undefined
lim_x→0+log_b(x) = - ∞
ln(e^x) = x

Body Mass Index or BMI Calculator Online

The Body Mass Index (BMI) Calculator can be used to calculate BMI value and corresponding weight status while taking age into consideration. Use the "Metric Units" tab for the International System of Units or the "Other Units" tab to convert units into either US or metric units. Note that the calculator also computes the Ponderal Index in addition to BMI, both of which are discussed below in detail.

Reference

BMI is a measurement of a person's leanness or corpulence based on their height and weight, and is intended to quantify tissue mass. Although BMI has limitations in that it is an estimate that cannot take body composition into account, it can be used as a general indicator of a healthy body weight based on a person's height. The value obtained from the calculation of BMI is widely used to categorize whether a person is underweight, normal weight, overweight, or obese depending on what range the value falls between. These ranges of BMI vary based on factors such as region and age, and are sometimes further divided into subcategories such as severely underweight or very severely obese. As previously mentioned however, due to a wide variety of body types as well as distribution of muscle, bone mass, and fat, BMI should be considered along with other measurements rather than being used as the sole method for determining a person's "healthy" body weight.

Body Mass Index Formula

Below are the equations used for calculating BMI in the International System of Units (SI) and the US customary system (USC) using a 5'10", 160-pound individual as an example:

USC Units: BMI = 703× mass (lbs) height2 (in)  = 703× 160 702  = 22.96 kg m2 SI, Metric Units: BMI =  mass (kg) height2 (m)  =  72.57 1.782  = 22.90 kg m2

Ponderal Index

The Ponderal Index (PI) is similar to BMI in that it measures the leanness or corpulence of a person based on their height and weight. The main difference between the PI and BMI is the cubing rather than squaring of the height in the formula (provided below). While BMI can be a useful tool when considering large populations, it is not reliable for determining leanness or corpulence in individuals. Although the PI suffers from similar considerations, the PI is more reliable for use with very tall or short individuals, while BMI tends to record uncharacteristically high or low body fat levels for those on the extreme ends of the height and weight spectrum. Below is the equation for computing the PI of an individual using USC, again using a 5'10", 160-pound individual as an example:

USC Units: PI =  height (in) ∛mass (lbs)  =  70 ∛160  = 12.89 in ∛lbs SI, Metric Units: PI =  mass (kg) height3 (m)  =  72.57 1.783  = 12.87 kg m3

 aa Adult BMI calculator based on 2013 AHA/ACC/TOS Guideline for the Management of Overweight and Obesity in Adults: A Report of the American College of Cardiology/American Heart Association Task Force on Practice Guidelines and The Obesity Society. BMI classification. World Health Organization. Adapted by Mayo Foundation for Medical Education and Research. Child BMI calculator based on clinical growth charts. Centers for Disease Control and Prevention. Adapted by Mayo Foundation for Medical Education and Research. Privacy assurance: Information that you enter won't be saved or sent to any website.

Scientific Calculator Online

Scientific calculator allows you to perform complex calculations using various trigonometric functions: sine, cosine, tangent, cotangent. Calculator can increase the number to a power, calculate the logarithm of the number. Basic commands (numbers, multiplication, division, addition, subtraction, equality, reset) can be entered using the mouse as well as using the numeric keypad (top or side). Detailed instructions for working with scientific calculator, see the bottom of the page.

0 sincostanDegRad sin-1cos-1tan-1πe xyx3x2ex10x y√x3√x√xlnlog ()1/x%n! 789+MS 456–M+ 123×M- 0.EXP÷MR ±RNDC=MC

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How to work with a scientific calculator:

• Functions of the standard buttons [ 0 ], [ 1 ], [ 2 ], ... [ 9 ] - standard numeric keypad; 
• [ 00 ] - key to enter the 2 zeros; 
• [ → ] - delete the last entered character is displayed; 
• [ +/- ] - changing the mathematical signs of the display on the opposite; 
• [ + ] - addition, 
• [ - ] - subtraction, 
• [ х ] - multiplication, 
• [ ÷ ] - division; 
• [ % ] - calculate interest; 
• [ M+ ] - stored in the memory with the sign [ + ] ; 
• [ M- ] - stored in the memory with the sign [ - ] ; 
• [ MR ] - get the contents of memory; 
• [ MC ] - clear the memory; 
• [ AC ] - reset the last value and clear the memory ; 
• [ C ] - reset the last digit of the; 

 Calculator buttons for performing trigonometric functions

• [ sin ] - sine of the angle, 
• [ cos ] - cosine of the angle, 
• [ tg ] - tangent of the angle, 
• [ ctg ] - cotangent of the angle; 
• [ asin ] - arc sine of the angle, 
• [ acos ] - arc cosine of the angle, 
• [ atg ] - arc tangent of the angle, 
• [ actg ] - arc cotangent of the angle; 
• [ π ] - mathematical constant, the ratio of the circumference to the diameter of the circle; 
• [ e ] - mathematical constant, the Euler number; 
• [ Xʸ ] - raise to higher power; 
• [ √ ] - square root; 

Examples of calculation of interest 
Calculation of percentage of the number of - 500 [ x ] 25 [ % ] Result - 125.
Deduction percentage of the number - 500 [ - ] 25 [ % ] Result - 375.
Adding percentage to the number - 500 [ + ] 25 [ % ] Result - 625.

Entering commands from the computer keyboard
To use the calculator you can use any keys: how keys are on top, and separate numeric keypad located on the right.

• To enter [ = ], you can use the [Enter]. 
• To erase the last character you can use the key to erase the last character [ Backspace ] (arrow keys). 
• To enter the sign [ + ] you can use either the [ + ] key at the top or press the [ + ] on the numeric keypad on the right. 
• To enter the sign [ - ] you can use either the [ - ] key at the top or press the [ - ] on the numeric keypad on the right. 
• To enter a [ x ] (multiplication) you can use the [ * ] key on the numeric keypad to the right or a combination of keys[ * ] and [ Shift ]. 
• To enter a [ ÷ ] (divide) you can use the [ / ] key on the numeric keypad to the right or a combination of keys [ : ] and [ Shift ].

F-Distribution

The F distribution calculator makes it easy to find the cumulative probability associated with a specified f value. Or you can find the f value associated with a specified cumulative probability. What are degrees of freedom? Degrees of freedom can be described as the number of scores that are free to vary. For example, suppose your friend tossed three dice, and the total score added up to 12. If your friend told you that he rolled a 3 on the first die and a 5 on the second, then you know that the third die must be a 4 (otherwise, the total would not add up to 12). In this example, 2 die are free to vary while the third is not. Therefore, there are 2 degrees of freedom. In many situations, the degrees of freedom are equal to the number of observations minus one. Thus, if the sample size were 20, there would be 20 observations; and the degrees of freedom would be 20 minus 1 or 19. What is f-value? An f value (also known as an f statistic) is a random variable that has an F distribution. Here are the steps required to compute an f value: Select a random sample of size n1 from a normal population, having a standard deviation equal to σ1. Select an independent random sample of size n2 from a normal population, having a standard deviation equal to σ2. The f value is the ratio of s12/σ12 and s22/σ22. Thus, f = [ s12/σ12 ] / [ s22/σ22]

Derivative Solver Calculator

The Derivative Calculator lets you calculate derivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. The Derivative Calculator supports computing first, second, .... fifth derivatives as well as differentiating functions with many variables (partial derivatives), implicit differentiation and calculating roots/zeros. You can also check your answers! Interactive graphs/plots help visualize and better understand the functions. How the Derivative Calculator Works For those with a technical background, the following section explains how the Derivative Calculator works. First, a parser analyzes the mathematical function. It transforms it into a form that is better understandable by a computer, namely a tree (see figure below). In doing this, the Derivative Calculator has to respect the order of operations. A specialty in mathematical expressions is that the multiplication sign can be left out sometimes, for example we write "5x" instead of "5*x". The Derivative Calculator has to detect these cases and insert the multiplication sign. The parser is implemented in JavaScript, based on the Shunting-yard algorithm, and can run directly in the browser. This allows for quick feedback while typing by transforming the tree into LaTeX code. MathJax takes care of displaying it in the browser. When the "Go!" button is clicked, the Derivative Calculator sends the mathematical function and the settings (differentiation variable and order) to the server, where it is analyzed again. This time, the function gets transformed into a form that can be understood by the computer algebra system Maxima.