How do you solve log_[4] (5x +1) - log_ [4] (x + 2) =1?

1 Answer
Apr 12, 2016

x = 7

Explanation:

Using the following color(blue)" laws of logarithms "

• log x - logy = log(x/y)

• log_b a = n hArr a = b^n

log_4((5x+1)/(x+2)) = 1 rArr (5x+1)/(x+2) = 4^1 = 4

solve : (5x+1)/(x+2) = 4

cross-multiply : 5x+1 = 4(x+2)

hence 5x + 1 = 4x+8 rArr x = 7