Question

Use the property of logarithms to evaluate the expression. No decimals.

Answer 1

If you want to solve for x, then the answer is x = 6*sqrt(2) where "sqrt" is shorthand for "square root"

Explanation:

All logs below are base 4

log(5) - log(18) = log(20) - 2*log(x)

log(5) - log(18) = log(20) - log(x^2)

log(5/18) = log(20/x^2)

5/18 = 20/x^2 ... raise both sides as exponents (base = 4); logs cancel

5x^2 = 18*20 ... cross multiply

5x^2 = 360

x^2 = 360/5 ... divide both sides by 5

x^2 = 72

x = sqrt(72) ... see note below.

x = sqrt(36*2)

x = sqrt(36)*sqrt(2)

x = 6*sqrt(2)

note: we only consider the positive solution for x because x cannot be negative. We cannot input negative x values into log(x). The domain of log(x) is x > 0. So we don't consider "plus/minus" for the square root.