the two expressions below have the same value when rounded to the nearest hundredth. log₅b log₉48 what is…

Explanation:

Step1: Calculate $\log_9 48$

Use the change - of - base formula $\log_a x=\frac{\ln x}{\ln a}$. So, $\log_9 48=\frac{\ln 48}{\ln 9}\approx\frac{3.8712}{2.1972}\approx1.76$.

Step2: Set $\log_5 b\approx1.76$

By the definition of logarithms, if $\log_5 b = 1.76$, then $b = 5^{1.76}$.

Step3: Calculate $b$

$b = 5^{1.76}\approx5^{\frac{44}{25}}=\sqrt[25]{5^{44}}\approx9.16$.

Step4: Calculate $\log b$ (assuming base 10)

$\log b=\log(5^{1.76}) = 1.76\log 5\approx1.76\times0.69897\approx1.23$.

Answer:

1.23