Question

Question #bb6f2

Answer 1

`x=log5/(log2)`

Explanation:

To solve we must use logs.

First we take logs to both sides (any base will do but let's use 10)

`therefore 2^x = 5` becomes `log2^x=log5`

We know from the laws of logs that:

`logb^x = xlogb`

`therefore` our new equation becomes

`xlog2=log5`

Now we just get `x` on it's own by dividing by `log2`

`therefore x=log5/(log2)`

This can be worked out on a calculator but I prefer to use exact values.