SOLUTION: Solve: 4^(1-x)=3*5^x I hope someone can help me, I have been trying to figure this one out for a while:( This is what I got : 4/3^x=3*5 4/3=(4*5)^x

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve: 4^(1-x)=3*5^x I hope someone can help me, I have been trying to figure this one out for a while:( This is what I got : 4/3^x=3*5 4/3=(4*5)^x       Log On

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Question 135161: Solve: 4^(1-x)=3*5^x
I hope someone can help me, I have been trying to figure this one out for a while:( This is what I got : 4/3^x=3*5
4/3=(4*5)^x
x=log(4/3)/log20
x=0.096... But my teacher marked it wrong :(
Found 2 solutions by stanbon, scott8148:
Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
Solve: 4^(1-x)=3*5^x
Take the log of both sides to get:
(1-x)log4 = log3 + xlog5
log4-xlog4 = log3 + xlog5
x(log4-log5) = log2-log4
x(log(4/5)) = log(1/2)
x = [log(1/2)]/[log(4/5)]
x = 3.1063
=================
Cheers,
Stan H.

Answer by scott8148(5880) About Me  (Show Source):
You can put this solution on YOUR website!
taking log __ (1-x)log(4)=log(3)+(x)log(5)

distributing __ log(4)-(x)log(4)=log(3)+(x)log(5)

subtracting log(3) and adding (x)log(4) __ log(4)-log(3)=(x)log(5)+(x)log(4)

factoring __ log(4)-log(3)=(x)(log(5)+log(4))

dividing by log(5)+log(4) __ (log(4)-log(3))/(log(5)+log(4))=x


your answer seems right, but I can't follow your solution...