Change of Base Formula

This formula can help us find the solutions to questions like:

2^x = 10 or log₂(10) = x

Formula:

log_bx = log_ax / log_ab

To get the answer using your calculator quickly, assume that a = 10.

This is because all the log buttons on our calculators are already based 10.

Using the formula we get:

x = log10 / log2

x = 3.322

Knowing this formula can be very useful, because in many questions it

Acts as a safety net if other methods fail.