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? log Subscript x Baseline x StartFraction log Subscript b Baseline x Over log Subscript b Baseline a EndFraction StartFraction log Subscript b Baseline a Over log Subscript b Baseline x EndFraction StartFraction log Subscript a Baseline b Over log Subscript x Baseline b EndFraction StartFraction log Subscript a Baseline x Over log Subscript b Baseline x EndFraction.

Answer 1

The expression that can be used to approximate the expression below is$log_a x = \frac{log_{b}a}{log_{b}x}$

• Given the logarithmic function expressed as $log_a x$, we need the log expression that is equivalent to the given expression.

• To do this, we will write the logarithm as a quotient to the same base. Using the base of 10, the expression can be written as;

$log_a x = \frac{log_{10}a}{log_{10}x}$

This is similar to the option c where the base of "b" was used as $log_a x = \frac{log_{b}a}{log_{b}x}$

Learn more on law of logarithms here: brainly.com/question/11587706