SOLUTION: Please help me solve this equation: 5^x= (7)(3^x)
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Question 320816: Please help me solve this equation: 5^x= (7)(3^x)
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Please help me solve this equation: 5^x= (7)(3^x)
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Take the log of both sides to get:
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x(log(5)) = log7 + x(log(3))
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Rearrange:
x[log(5)-log(3)] = log(7)
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x = log(7)/[log(5/3)]
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x = 3.8093
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cheers
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Take the natural log of both sides (actually, it can be the log to any base as it won't matter in the end).
\ =\ \ln\left(7\,\cdot\,3^x\right))
The log of the product is the sum of the logs:
\ =\ \ln\left(7\right)\ +\ \ln\left(3^x\right))
Add )
to both sides:
\ -\ \ln\left(3^x\right)\ =\ \ln\left(7\right))
Then use:
\ =\ n\log_b(x))
so:
\ -\ x\ln\left(3\right)\ =\ \ln\left(7\right))
Factor:
\ -\ \ln\left(3\right)\right)\ =\ \ln\left(7\right))
The difference of the logs is the log of the quotient:
\ =\ \ln\left(7\right))
Finally, multiply by })
}{\ln\left(\frac{5}{3}\right)})
Use the calculator for a numerical approximation if necessary.
John
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