Pythagorean theorem
Find a missing side in a right triangle. Choose whether the missing side is the longest hypotenuse or one of the two perpendicular legs.
MAKE THE FORMULA CLEAR
Logarithm
Find the exponent needed to raise a base to a positive number. This is different from dividing the number by the base.
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Logarithm result
2
For base 10 and value 100, the answer 2 means 10² = 100, not 100 divided by 10.
Worked steps
- log_10(100)＝ln(100)／ln(10)
logₐ(x) = ln(x) / ln(a). The base must be positive and not 1; the argument must be positive.
Method and scope
Log base a of x equals natural log of x divided by natural log of a. The base must be positive and not one, and x must be positive.
The answer is an exponent and has no physical unit. A value between zero and one can have a negative logarithm when the base exceeds one.
Zero and negative arguments are outside the real logarithm domain. The entered approximation of e and displayed numeric answers are finite decimal approximations.
What this helps you do
Find the exponent needed to raise a base to a positive number. This is different from dividing the number by the base.
What to enter
Start with base, then fill the other relevant fields in the units shown. The field hints explain the required format and examples.
How the calculation works
Log base a of x equals natural log of x divided by natural log of a. The base must be positive and not one, and x must be positive.
Worked example
Base 10 with x = 1,000 gives 3 because 10 cubed is 1,000. For a natural logarithm, enter base 2.718281828459045 rather than the letter e.
Understanding the answer
The answer is an exponent and has no physical unit. A value between zero and one can have a negative logarithm when the base exceeds one.
Scope and limitations
Zero and negative arguments are outside the real logarithm domain. The entered approximation of e and displayed numeric answers are finite decimal approximations.