SOLUTION: I need a lot of help on.... log base 4 (x+1) - log base 4x=3

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Question 600332: I need a lot of help on.... log base 4 (x+1) - log base 4x=3
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%28x%2B1%29%29-log%284%2C%28x%29%29+=+3 Start with the given equation

log%284%2C%28%28x%2B1%29%2Fx%29%29+=+3 Condense the logs using the identity log%28b%2C%28X%29%29+-+log%28b%2C%28Y%29%29+=+log%28b%2C%28X%2FY%29%29

%28x%2B1%29%2Fx+=+4%5E3 Convert to exponential form.

%28x%2B1%29%2Fx+=+64 Cube 4 to get 64

x%2B1+=+64x Multiply both sides by x

1+=+64x-x Subtract x from both sides

1+=+63x Combine like terms

1%2F63+=+x Divide both sides by 63 to isolate x

x+=+1%2F63 Flip the equation.


So the solution is x+=+1%2F63

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
log base 4 (x+1) - log base 4x=3
------
log4(x+1) - log4(x) = 3
----
log4[(x+1)/x] = 3
----
(x+1)/x = 4^3
-----
(x+1)/x = 64
---
x+1 = 64x
63x = 1
x = 1/63
===============
Cheers,
Stan H.