Question

If log32=1.505, then what is the value of log1000^32?

A:.000502
B: .001505
C: 1,505
D: 0.502

I am not sure what it could be. I think A?

Answer 1

D: 0.502

Explanation:

Answer 2

ANSWER


`log_(1000)(32) = 0.502`

EXPLANATION

We were given that,


`log(32) = 1.505`

Recall that the base is 10. So we can rewrite to get,


`log_(10)(32) = 1.505 - - - (1)`

We now write the logarithm we are trying to evaluate also as logarithm to base 10.


`log_(1000)(32) = log_{ {10}^(3) }(32)`

Recall that,

`log_{ {p}^(q) }(m) = (1)/(q) log_(p)(m)`

We apply this law to obtain,


`log_(1000)(32) = (1)/(3) log_( 10 )(32)`

We now substitute equation 1 into this last equation to get,


`log_(1000)(32) = (1)/(3) (1.505)`

This simplifies to,


`log_(1000)(32) = 0.502`

The correct answer is option D.