# solve for the unknown quantity log_5 16 [if needed, use only 4 digit log tables (base 10)]

### 1 Answer | Add Yours

here base used is 5 and we do not know the value of `log_(5) 16`

therefore we have to convert to a expression with a base that we know the values. That is the base of 10.

We know that

`log_(a) x =(log_(b) x)/(log_(b) a)`

Therefore we can convert the expression as follow,

`log_(5) 16 =(log_(10) 16)/(log_(10) 5)`

using the log table(base 10) we can get

`log_(10) 16 = 1.2041`

`log_(10) 5 = 0.6990`

`hence`

` ` `log_(5) 16 =(log_(10) 16)/(log_(10) 5) = 1.2041/0.6990 = 1.7226`

**therfore the answer,**

**`log_(5) 16 = 1.7226`**