Question

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a. 1 and b.

Answer 1

Answer:it’s A

Step-by-step explanation: I took the quiz

Answer 2

The required "option A) $\dfrac{\log_{b}x}{\log_{b}a}$" is correct.

Step-by-step explanation:

We have,

$\log _{a}x$

To find, the value of $\log _{a}x$ = ?

∴ $\log _{a}x$ , where a, b  and x are positive

a ≠ 1 and b ≠ 1

We know that,

The logarithm identity,

$\log_{p}m=\dfrac{\log_{y}m}{\log_{y}p}$

∴ $\log _{a}x$ = $\dfrac{\log_{b}x}{\log_{b}a}$

Where, b is the common base of logarithm

∴ The value of $\log _{a}x$ = $\dfrac{\log_{b}x}{\log_{b}a}$

Thus, the required option A) $\dfrac{\log_{b}x}{\log_{b}a}$ is correct.