SOLUTION: Solve for x, and write the EXACT answer using base-10 log.
(13^(-x+6))=(15^(-10x))
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Question 1053172: Solve for x, and write the EXACT answer using base-10 log.
(13^(-x+6))=(15^(-10x))
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Note: I follow the convention that 
means 
Take the log of both sides
\ =\ \log\left(15^{-10x}\right))
Use \ =\ n\log_b(x))
\log\left(13\right)\ =\ (-10x)\log\left(15)\right))
}{\log(13)}\ =\ \frac{\log\left(15^{10}\right)}{\log(13)})
}{\log(13)})
}{\log(13)}\ =\ \frac{\log(13)}{\log(13)}\ -\ \frac{\log\left(15^{10}\right)}{\log(13)}\ =\ \frac{\log(13)\ -\ \log\left(15^{10}\right)}{\log(13)})
The difference of the logs is the log of the quotient:
}{\log(13)})
}{6\log(13)}\ =\ \frac{\log\left(\frac{13}{15^{10}}\right)}{\log(13^6)})
Take the reciprocal
}{\log\left(\frac{13}{15^{10}}\right)}\ =\ \frac{\log(4,826,809)}{\log\left(\frac{13}{576,650,390,625}\right)})
John
My calculator said it, I believe it, that settles it
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