Rewrite the given equation without logarithms. DO NOT solve for x

Question

Log₅(x+22)- log₅(x-2)=2

Answer 1

log5(x+22) - log5(x-2) = 2

the difference in logs is equal to the log of the quotient

log5[(x+22)/(x-2)] = 2

rewrite in exponential form

(x+22)/(x-2) = 5^2

(x+22)/(x-2) = 25

as a check on the answer

solve for x and see if it works when you plug it into the original log equation:

x+22 = 25(x-2)

x+22 = 25x -50

24x = 72

x = 72/24 = 3

x=3

log5(3+22) - log5(3-2)

=log5(25) - log5(1)

=2 - 0

= 2