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:
[tex]log_c(d) = \frac{log_h(d)}{log_h(c)}[/tex]
We also know that:
[tex]log_{10}(c)[/tex] is also written as [tex]log(c)[/tex].
Then, we can write:
[tex]log_5(b) = \frac{log(b)}{log(5)}[/tex]
Then:
[tex]log_5(b) = log_9(48)[/tex]
So:
[tex]log_{9}(48) = \frac{log(b)}{log(5)}[/tex]
[tex]log(b) = log(5)[log_9(48)]\\\\log(b) = 0.69897[1.7619]\\\\log(b) = 1.23[/tex]
