# Logarithms

Whenever you see the words log or logarithms write down the following:

Log_2(8)=3

And write down

What is the power on 2 that gives 8

## Logs explained

Log_2(8)=3

This says:

What is the power on 2 that gives 8

2^? = 8

i.e. 2^3 = 8

## For any log

From the above Log_ab

Logarithm is the power on “a” that gives the result “b”

Examples

1.  What is Log_3 81

Write out what you know

We know Log_2 (8) = 3

and this means “what is the power of 2 that gives 8”

and that equals 3

Therefore  Log_3 81

This says what is the power on 3 that gives 81

 3^? = 81 3times3 = 9 3times3times 3 = 27 3\times 3\times 3\times 3 = 81 (4\ t\im\es)

Therefore Answer: 4 is the power on 3 that gives 81

That is 3^4 = 81