Question

Which of the following is true regarding the solutions to the logarithmic equation below? 2 log Subscript 6 Baseline (x) = 2. log Subscript 6 Baseline (x squared) = 2. x squared = 6 squared. x squared = 36. x = 6, negative 6. x = 6 and x = negative 6 are true solutions x = 6 and x = negative 6 are extraneous solutions x = 6 is a true solution and x = negative 6 is an extraneous solution x = 6 is an extraneous solution and x = negative 6 is a true solution

Answer 1

Option c: x=6 is a true solution and x=-6 is an extraneous solution.

Explanation:

The equation is $2 \log _{6} x=2$

Dividing both sides of the equation by 2, we get,

$\frac{2 \log _{6}(x)}{2}=\frac{2}{2}$

Simplifying,

$\log _{6}(x)=1$

Since, we know by the logarithmic definition, if $\log _{a}(b)=c$, then $b=a^{c}$

Using this definition, we have,

$x=6^{1}$

Hence, $x=6$

Now, let us verify if $x=6$ is the solution.

Substitute $x=6$ in the equation $2 \log _{6} x=2$ to see whether both sides of the equation are true.

We have,

$2 \log _{6}(6)$

Using the log rule, $\log _{a}(a)=1$

We have,

$2*1=2$

Hence, both sides of the equation are equal.

Thus, $x=6$ is the true solution.

Answer 2

Answer:

C is the answer i got it correct

Step-by-step explanation: