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

Answer:

B. 1.23

Step-by-step explanation:

Answer 2

Answer:

The answer is the second option: 1.23

Step-by-step explanation:

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

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

$log_c(d) = \frac{log_h(d)}{log_h(c)}$

We also know that:

$log_{10}(c)$ is also written as $log(c)$.

Then, we can write:

$log_5(b) = \frac{log(b)}{log(5)}$

Then:

$log_5(b) = log_9(48)$

So:

$log_{9}(48) = \frac{log(b)}{log(5)}$

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