Question

Which of the following is true regarding the solutions to the logarithmic equation below? 2log3(x)=4 log3(x^2)=4 x^2=3^4 x^2=81 x=9,-9

Answer 1

Answer:

The answer is d on egde

Step-by-step explanation:

I just got it right

Answer 2

Answer:

$x=-9$ is an extraneous solution: True

$x=9$ is the only solution: True

Step-by-step explanation:

The given logarithmic equation is: $2\log_3x=4$

Apply the property $n\log_ab=\log_ab^n$ to the LHS to get: $\log_3x^2=4$

We rewrite the corresponding indicial expression to get:

$x^2=3^4$

Simplify the RHS to get:

$x^2=81$

Take square root to get:

$x=\pm 9$

Since the domain of the logarithmic function is positive real numbers, the only solution is $x=9$