The following logarithmic expression can be used to approximate the given expression,
![\frac{log_{b} x}{log_{b} a}](https://tex.z-dn.net/?f=%5Cfrac%7Blog_%7Bb%7D%20x%7D%7Blog_%7Bb%7D%20a%7D)
Finding the Logarithmic Expression
It is given that for all positive numbers a, b, and x on the condition that a≠1 and b≠1.
Now, for positive values of m and n, we have the following logarithmic expression,
![\frac{log_{m} x}{log_{n} a}](https://tex.z-dn.net/?f=%5Cfrac%7Blog_%7Bm%7D%20x%7D%7Blog_%7Bn%7D%20a%7D)
Here, m, n and x are all positive numbers.
The logarithmic property imposes that m and n are not equal to 1.
So, by substituting the values m and n by a and b respectively, we get the following logarithmic expression,
![\frac{log_{b} x}{log_{b} a}](https://tex.z-dn.net/?f=%5Cfrac%7Blog_%7Bb%7D%20x%7D%7Blog_%7Bb%7D%20a%7D)
Therefore,
is the required expression.
Learn more about a logarithmic expression here:
brainly.com/question/24211708
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