SOLUTION: 4^(1-9x)=3^x Please help me find the value of X

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Question 959166: 4^(1-9x)=3^x
Please help me find the value of X
Found 3 solutions by josgarithmetic, lwsshak3, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E1%2A4%5E%28-9x%29=3%5Ex?
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ln%284%5E%281-9x%29%29=ln%283%5Ex%29
%281-9x%29ln%284%29=x%2Aln%283%29
%281-9x%29=x%2Aln%283%29%2Fln%284%29
1-9x-x%2Aln%283%29%2Fln%284%29=0
-9x-x%2Aln%283%29%2Fln%284%29=1
x%28ln%283%29%2Fln%284%29-9%29=1
highlight%28x=1%2F%28ln%283%29%2Fln%284%29-9%29%29

A better form may be more desired.
x=%281%2F%28ln%283%29%2Fln%284%29-9%29%29%28ln%284%29%2Fln%284%29%29
highlight%28x=ln%284%29%2F%28ln%283%29-9%2Aln%284%29%29%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
4^(1-9x)=3^x
Please help me find the value of X
(1-9x)log4=xlog3
1-9x=xlog3/log4
1-9x=0.7925x
9.7925x=1
x=1/(9.7925)
x≈0.1021

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

4^(1-9x)=3^x
Please help me find the value of X
4%5E%281+-+9x%29+=+3%5Ex

log+4%5E%281+-+9x%29+=+log+3%5Ex -------- Taking log of both sides

1 - 9x * log 4 = x log 3

%281+-+9x%29%2Fx+=+log+3%2Flog+4

%281+-+9x%29%2Fx+=+.792481

.792481x = 1 – 9x ------- Cross-multiplying

.792481x + 9x = 1

9.792481x = 1

x+=+1%2F9.792481, or highlight_green%28x+=+0.102119+%29