SOLUTION: solve the exponential equation. express irrational solutions as decimals correct to the nearest thousandth. 2^x-2=3^2x
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Question 627046: solve the exponential equation. express irrational solutions as decimals correct to the nearest thousandth. 2^x-2=3^2x
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Note: 
Take the natural log of both sides (actually, any base will do as long as you use the same base on both sides of the equation)
\ =\ \ln\left(9^x\right))
Use \ =\ n\log_b(x))
to write:
\ln\left(2\right)\ =\ x\ln\left(9\right))
Multiply both sides by the reciprocal of )
\ =\ x\frac{\ln\left(9\right)}{\ln\left(2\right)})
terms on the left, constants on the right, just like any other single variable equation.
}{\ln\left(2\right)}\ =\ 2)
Factor out
}{\ln\left(2\right)}\right)\ =\ 2)
Multiply by the reciprocal of the coefficient on
}{\ln\left(2\right)}})
The rest is just calculator work.
John
My calculator said it, I believe it, that settles it
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