Question

log (x^2+2x) = log (7x+24)

Answer 1

taking the logs out
x^2 + 2x = 7x + 24
x^2 -5x - 24 = 0
factoring
(x-8)(x+3) = 0
x= 8 or -3

Answer 2

do the logs cancel each other out?

Answer 3

in a way they - if the log of 2 is equal to log of x then by logic x = 2

Answer 4

right?

Answer 5

The logs don't 'cancel' but if the left side equals the right side, then you can raise 10 to the power of each side and you should still have equality.
\[log (x^2+2x) = log (7x+24)\]\[\implies 10^{log (x^2+2x)} = 10^{log (7x+24)}\]\[\implies x^2+2x = 7x+24\]