Log x = log(x + 3) - log(x - 1)

First note that log(x) is defined only for x > 0; log(x + 3) for x > -3; and log(x - 1) for x > 1. So if we find any solutions x ≤ 1, these will be extraneous.

Condense the right side:

log(x) = log((x + 3) / (x - 1))

Let b be the base of the logarithm. Then writing both sides as powers of this b simplifies the equation to

b^log(x) = b^log((x + 3) / (x - 1))

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

Solve for x :

x (x - 1) = x + 3

x ² - x = x + 3

x ² - 2x - 3 = 0

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

x - 3 = 0   or   x + 1 = 0

x = 3   or   x = -1

We throw out x = -1 because it's less than 1, so the only (real) solution is x = 3.

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

step-by-step explanation:

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