Precalculus math problem?

Question

log(-x) + log(-2x-5) = log(7)?

Answer 1

log(-x) + log(-2x - 5) = log7

Recall : logarithm formula loga + logb = logab

Substitute a = -x and b = -2x - 5 in the above logarithm formula

log(-x)(-2x - 5) = log7

log(2x^2 + 5x ) = log7

Remove logarithm to each side

2x^2 + 5x = 7

2x^2 + 5x - 7 = 0

2x^2 -2x + 7x - 7 = 0

2x(x - 1) + 7(x - 1) = 0

Take out common term x - 1

(x - 1)(2x + 7) = 0

x - 1 = 0 or 2x + 7 = 0

x = 1 or x = -7 / 2

x = -7 / 2 , 1.