SOLUTION: Solve the exponential equation.
4^(x-1)=3^(2x)
Algebra.Com
Question 434696: Solve the exponential equation.
4^(x-1)=3^(2x)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
First note: 
so:
Take the log of both sides (any base, it doesn't matter)
\ =\ \ln\left(9^x\right))
Use the laws of logs:
\ln\left(4\right)\ =\ x\ln\left(9\right))
Distribute and collect like terms:
\ -\ x\ln(9)\ =\ \ln(4))
Factor out the x
\ -\ \ln(9)\right)\ =\ \ln(4))
The difference of the logs is the log of the quotient:
\right)\ =\ \ln(4))
Solve for x:
}{\ln\left(\frac{4}{9}\right)})
Which is the exact simplifed answer, or you can use your calculator to get a numeric approximation to whatever precision is appropriate to your application.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
solve the exponential equation... (answered by stanbon)
Solve the following exponential equation: 3^(2x) -4(3^x) + 3 = 0 (answered by KMST)
Solve the exponential equation algebraically. Show steps... (answered by stanbon)
Solving the exponential equation :... (answered by lwsshak3)
solve the exponential equation... (answered by Alan3354,ikleyn,MathTherapy)
solve: 3^-2x+1 * 3^-2x-3= 3^-x
exponential equation not requiring... (answered by stanbon)
Solve the exponential equation algebraically... (answered by josgarithmetic)
Solve the exponential equation.
3^(x^2+5x) =... (answered by josmiceli)
Solve the exponential equation.
2x = 1/2
3x = 1/27
2-x = 16
4x = 0.5
8x =... (answered by Alan3354,lynnlo)
