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

1 Answer
Jim G.
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 #

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