SOLUTION: Condense.... log3 (5x + 3) = 2 + log3 (x-1)

Question 62980This question is from textbook college algebra
: Condense....
log3 (5x + 3) = 2 + log3 (x-1) This question is from textbook college algebra

Answer by uma(370) (Show Source): You can put this solution on YOUR website!
log 3 (5x+3) = 2 + log 3 (x-1)
adding - log 3 (x-1) to both the sides we get,
log 3 (5x+3) - log 3 (x-1) = 2
==> log 3 [(5x+3)/(x-1)] = 2 [as loga - logb = log(a/b)]
==> 5x+3/(x-1) = 3^2 [writing in the exponential form]
==> (5x+3)/(x-1) = 9
==> 5x + 3 = 9(x-1)
==> 5x + 3 = 9x - 9
==> 5x + 3 - 9x = 9x - 9x - 9
==> - 4x + 3 = -9
==> - 4x + 3 - 3 = -9 - 3
==> - 4x = -12
==> -4x/-4 = - 12/-4
==> x = 3
Thus x = 3
Good Luck!!!
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