Question

The two expressions below have the same value when rounded to the nearest hundredth. log5 b log9 48 What is the approximate value of log b to the nearest hundredth? 0.93 1.23 9.16 65.53

Answer 1

The answer is the second option: 1.23

Explanation:

To solve this problem we use the logarithmic base change property.

Let c, d and h be positive real numbers then:

`log_c(d) = (log_h(d))/(log_h(c))`

We also know that:

`log_(10)(c)` is also written as
`log(c)`.

Then, we can write:

`log_5(b) = (log(b))/(log(5))`

Then:

`log_5(b) = log_9(48)`

So:

`log_(9)(48) = (log(b))/(log(5))`

`log(b) = log(5)[log_9(48)]\\\\log(b) = 0.69897[1.7619]\\\\log(b) = 1.23`