Question

Which of the following is true regarding the solutions to the logarithmic equation below? 2 log Subscript 3 Baseline (x) = 4. Log Subscript 3 Baseline (x squared) = 4. X squared = 3 Superscript 4. X squared = 81. X = 9, negative 9 x = 9 and x = negative 9 are true solutions x = 9 and x = negative 9 are extraneous solutions x = 9 is an extraneous solution and x = negative 9 is a true solution x = 9 is a true solution and x = negative 9 is an extraneous solution.

Answer 1

Using logarithmic function concepts, it is found that the correct statement is:

x = 9 is a true solution and x = -9 is an extraneous solution.

What is a logarithmic function?

A logarithmic function is modeled by:

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

It means that:

$b^a = x$

In this problem, we have that:

$2\log_{3}{x} = 4$

Applying the power property:

$\log_3{x^2} = 4$

Applying the definition:

$x^2 = 3^4$

$x^2 = 81$

$x = \pm 9$

As the logarithm function is defined only for positive values, the correct statement is:

x = 9 is a true solution and x = -9 is an extraneous solution.

You can learn more about logarithmic function concepts at brainly.com/question/26302013