SOLUTION: 4^x+5 = 6 so far I have log 4^x+5 = log 6 (x+5)log 4 = log 6 not sure where to go from here, any help is appreciated thanks sherry

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 4^x+5 = 6 so far I have log 4^x+5 = log 6 (x+5)log 4 = log 6 not sure where to go from here, any help is appreciated thanks sherry      Log On


   

Question 171030: 4^x+5 = 6
so far I have
log 4^x+5 = log 6
(x+5)log 4 = log 6
not sure where to go from here, any help is appreciated
thanks
sherry
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
First, you ought to use parentheses to show that the exponent is (x+5).
4%5E%28x%2B5%29+=+6 Take the logarithm of both sides.
log%284%29%5E%28x%2B5%29+=+log%286%29 Apply the power rule to the left side.
%28x%2B5%29%2Alog%284%29+=+log%286%29 Divide both sides by log%284%29
x%2B5+=+%28log%286%29%29%2Flog%284%29 Evaluate the right side.
x%2B5+=+1.29248 Subtract 5 from both sides.
x+=+-3.70752
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At first, because you have no parentheses in 4^x+5 = 6, I assumed that the problem was:
4%5Ex+%2B+5+=+6 If this is what you really meant to write, then: Subtract 5 from both sides.
4%5Ex+=+1 Take the log of both sides.
log%284%5Ex%29+=+log%281%29 Apply the power rule to the left side.
x%2Alog%284%29+=+log%281%29 Divide both sides by log%284%29
x+=+%28log%281%29%29%2Flog%284%29 But log%281%29+=+0, so...
x+=+0
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