SOLUTION: So I have to solve this equation by using logarithms. I am so lost. 2.5^x=34.1^(2x+7)

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Question 1117690: So I have to solve this equation by using logarithms. I am so lost.
2.5^x=34.1^(2x+7)
Found 3 solutions by Alan3354, rothauserc, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
2.5^x=34.1^(2x+7)
x*log(2.5) = (2x+7)*log(34.1)
x*log(2.5) = 2x*log(34.1) + 7*log(34.1)
x*log(2.5) - 2x*log(34.1) = 7*log(34.1)
x*(log(2.5) - 2log(34.1)) = 7*log(34.1)
x = 7log(34.1)/(log(2.5) - 2log(34.1))
All the logs are just constants.
x =~ -2.55439411
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
2.5^x = 34.1^(2x+7)
:
rewrite both sides of = using fractions
:
(5/2)^x = (341/10)^(2x+7)
:
take natural logarithms of both sides and use the identity log(a^b) = b * log(a)
:
log(5/2) * x = log(341/10) * 2x+7
:
rewrite terms on the right side of =
:
log(5/2) * x = 2 * log(341/10) * x + 7 * log(341/10)
:
subtract 2 * log(341/10) * x from both sides of = and isolate x
:
(log(5/2) - 2 * log(341/10)) * x = 7 * log(341/10)
:
now solve for x
:
x = (7 * log(341/10)) / (log(5/2) - 2 * log(341/10))
:
****************************************************
x = -4.0221
****************************************************
:
Answer by MathTherapy(10559)   (Show Source): You can put this solution on YOUR website!

So I have to solve this equation by using logarithms. I am so lost.
2.5^x=34.1^(2x+7)
TOTALLY IGNORE the suggestion by that person to CONVERT the decimals to fractions. That doesn't make ANY SENSE, at all!!



 ------ Taking log of both sides

x log (2.5) = (2x + 7) * log (34.1)





3.8517(2x + 7) = x ------- Cross-multiplying

7.7034x + 26.9619 = x

26.9619 = x - 7.7034x

26.9619 = - 6.7034x

 

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