Question 438992: (4/3)^1-x =5^x
Please show me how to solve this showing all steps. I tried taking the ln of both sides and ended up with x=.47, which is wrong. I know the answer is x=0.15, but am not sure how to get there. Below I will show my original work done so you can see that I have tried, even though I am certain it is incorrect.
(4/3)^1-x=5^x
(1-x) ln4/3=x ln5
ln4/3-(ln4/3)x=(ln5)x
x= ln4/3 =.47
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ln5 + ln4/3
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! I know the answer is x=0.15, but am not sure how to get there. Below I will show my original work done so you can see that I have tried, even though I am certain it is incorrect.
(4/3)^(1-x) = 5^x
(1-x)ln(4/3) = x ln5
ln4/3-(ln4/3)x=(ln5)x
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[ln(5)+ln(4/3)]x = ln(4/3)
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[ln[(20/3)]x = ln(4/3)
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x = [ln(4/3)]/[ln(20/3)]
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x = 0.2877/1.8971
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x = 0.1516...
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Cheers,
Stan H.
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