Solve. log2 (8x) - log2 (x^2-1) = log2 3

x = 3

Taking the antilog, the equation becomes ...

... 8x/(x^2 -1) = 3

Multiplying by the denominator, you have ...

... 8x = 3(x^2 -1)

Subtracting the left side to put into standard form gives ...

... 3x^2 -8x -3 = 0

This can be factored as ...

... (3x +1)(x -3) = 0

so the values of x that make these factors zero are ...

... x = -1/3 . . . and . . . x = 3

The original equation requires x > 1, so the only viable solution here is ...

... x = 3

_____

We can also solve this graphically to get the same result.

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.