Logarithms

To understand logarithms, you should first understand exponents because a logarithm is an exponent.

Finding a logarithm (base $b$ ) of a number is like answering the question:

To what power do I have to raise $b$ to get this number?

Or, in math notation:

$\log_{b} a = x$ means $b^{x} = a$

Examples:

$\log_{7} 49 = 2$ , since $7^{2} = 49$

$\log_{2} 32 = 5$ , since $2^{5} = 32$

$\log_{10} 0.01 = - 2$ , since $10^{- 2} = 0.01$

This can be a little confusing. Remember that the base in the logarithm equation (the small subscripted number) is also the base in the power equation (the number raised to the power), and they stay on the left side.

In real life, we usually only use two bases: $\log_{10}$ , also called the common logarithm , and $\log_{e}$ , where $e \approx 2.71828$ , also called the natural logarithm .

$\log_{10} x$ is usually written $\log x$ , with the base understood to be $10$ . $\log_{e} x$ is written $\ln x$ .

Logarithms

Download our free learning tools apps and test prep books