<h3>
Answer: E) y = -25/13</h3>
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Work Shown:
Let x = log(y+2)
The given equation becomes
4x = 3x-log(13)
Solving for x leads to
4x-3x = -log(13)
x = -log(13)
Then substituting gets us
log(y+2) = -log(13)
log(y+2) = log(13^(-1)) .... use the rule that A*log(B) = log(B^A)
log(y+2) = log(1/13)
y+2 = 1/13 ................. used the rule if log(A) = log(B), then A = B
y = (1/13) - 2
y = (1/13) - (26/13)
y = (1-26)/13
y = -25/13 .... answer is choice E
For each step, the logs are the same base. The base doesn't matter. It can be base 10 or base 2 or base e. As long as the base stays consistent is all that matters. Also, the base cannot be 1, 0 or a negative number. The base can be any other real number.
