Question 618666: Solve each equation: Round answers to the nearest thousandth.
4^(6x-1)=5^(x+4)
I origionally attepted to set the equation to a logarithim but i was not sure how to remove the X from both powers, i got to
logbase4 5^(x+4)=6x-1 but got lost with the x+4, but now while typeing this i think i may use power property? (x+4)logbase4 5=6x-1? Then I get lost with how to remove the log from the problem, thanks -Brandon
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! 4^(6x-1)=5^(x+4)
take the log of both sides:
log(4^(6x-1))= log(5^(x+4))
(6x-1)log(4)= (x+4)log(5)
(6x)log(4) - log(4) = xlog(5)+4log(5)
(6x)log(4) = xlog(5)+4log(5)-log(4)
(6x)log(4)-xlog(5) = 4log(5)-log(4)
x[6log(4)-log(5)] = 4log(5)-log(4)
x = [4log(5)-log(4)] / [6log(4)-log(5)]
x = 2.1938 / 2.9134
x = 0.753
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