Question

What are the solutions to log subscript 6 baseline (x squared 8) = 1 log subscript 6 baseline (x)

Answer 1

The solution of the logarithmic equation is given by the antilog. Then the value of x is 2 and 4.

What is a factorization?

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The logarithmic equation is given below.

$\log _6(x^{2} +8)= 1+ \log _6x\\\\\log _6(x^{2} +8)= \log_66+ \log _6x\\\\\log _6(x^{2} +8)= \log _66x$

Take antilog, then we have

$\begin{aligned} x^{2} +8 &= 6x\\\\x^2 -6x + 8 &= 0\\\\x^2 -4x - 2x +8 &=0\\\\(x-4)(x-2) &= 0\\\\x&= 2, 4\end{aligned}$

Then the value of the x is 2 and 4.

More about the factorization link is given below.

brainly.com/question/6810544