Question

Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a not-equals 1 and b not-equals 1?

Answer 1

The following logarithmic expression can be used to approximate the given expression,

$\frac{log_{b} x}{log_{b} a}$

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,

$\frac{log_{m} x}{log_{n} a}$

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,

$\frac{log_{b} x}{log_{b} a}$

Therefore, $\frac{log_{b} x}{log_{b} a}$ is the required expression.

Learn more about a logarithmic expression here:

brainly.com/question/24211708

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