Please help with Steps

Question

solve for x

log₂ (8x) - log₂ (x² - 1) = log₂3

Answer 1

The equation is of the form A = B, so we are going to turn it into 2^A = 2^B and solve.

2^(log₂^{8x - log}₂^{(x^2 - 1))} = 2^(log₂³⁾

The left hand side shows a subtraction in the exponent, so we can turn that into a division such that

2^(log₂^8x) / 2^log₂^{(x^2 - 1)} = 2^(log₂³⁾

Using the property a^log_a^(c) = c,

8x / (x² - 1) = 3

8x = 3x² - 3

3x² - 8x - 3 = 0

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

We can see that x = 3 OR x = -1/3, but we cannot accept the solution x = -1/3 because it would make the logarithmic argument (x² - 1) negative, which is undefined. Thus, we accept x = 3 as the solution.