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

The answer is d on egde

Explanation:

I just got it right

Answer 2

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

`x=9` is the only solution: True

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`