SOLUTION: Find the exact solution:
3^3x-4=5^x
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Question 363175: Find the exact solution:
3^3x-4=5^x
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I have to assume that you meant:
Since the other (equally valid per your notation) interpretation, namely:
Can only be solved by numerical methods and therefore an exact solution cannot be determined.
Step 1: Take the log of both sides. Natural log or base 10 (or any other base you like), it doesn't matter.
\ =\ \ln\left(5^x\right))
Use
\ =\ n\log_b(x))
to write:
\ln\left(3\right)\ =\ x\ln\left(5\right))
Multiply both sides by })
}{\ln\left(3\right)})
Add 
and }{\ln\left(3\right)})
to both sides:
}{\ln\left(3\right)}\ =\ 4)
Factor out an 
}{\ln\left(3\right)}\right)\ =\ 4)
Multiply both sides by }{\ln\left(3\right)}})
}{\ln\left(3\right)}})
John
My calculator said it, I believe it, that settles it
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