Question

Solve the equation below for x:
log(5X)+log(x-1)=2

A. There is no solution.

B. x = 5

C. x = 4; x = -4

D. x = 5/2

Answer 1

first combine them:

log(5x(x-1)) = 2

10^2 = 5x(x-1)

5x^2 - 5x - 100 = 0

x^2 - x - 20 = 0

(x+4)(x-5) = 0

x=-4 or x=5

but you can't take the log of a negative number, so -4 doesn't work.

so the answer is 5.