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The following logarithmic expression can be used to approximate the given expression,
[tex]\frac{log_{b} x}{log_{b} a}[/tex]
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,
[tex]\frac{log_{m} x}{log_{n} a}[/tex]
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,
[tex]\frac{log_{b} x}{log_{b} a}[/tex]
Therefore, [tex]\frac{log_{b} x}{log_{b} a}[/tex] is the required expression.
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