mathematics > csec > additional mathematics > algebra and functions > logarithms

Logarithms

The log of a number is the power to which the base must raised in order to produce that number.

Given the exponential form: $$a^x=b$$ $a$ is the base, $x$ is the exponent and $b$ is the given number. We can rewrite this in log form: $$log_{a}b=x$$ We read this as log base a of b is x. Notice how $x$ is the power in the exponential form. $x$ is the log (the log is the power).

We know that $3^2=9$ therefore in log form this will be $$log_{3}9=2$$ 3 is the base, 9 is the given number and 2 is the power (therefore log base 3 of 9 is 2 because the log is the power and 2 is the power).

Challenge

Given the exponential form $4^2=16$, what is the log form? (Tap/click an answer below)

Given the logarithmic form $log_{3}81=4$, what is the exponential form? (Tap/click an answer below)

Find the value of $x$ in $log_{12}x=2$ (Tap/click an answer below)

The logarithm is (Tap/click an answer below)

If $a^0=1$ then $log_{a}1=?$ (Tap/click an answer below)

Laws of logs

There are three (3) basic laws of logs.

The sum of two logs

$log_{a}b+log_{a}c=log_{a}bc$

The difference of two logs

$log_{a}b-log_{a}c=log_{a}\frac{b}{c}$

The scalar multiple of a log

$nlog_{a}b$=$log_{a}b^n$