Solve for x to 3 decimal places: 3^2x= 4^(1-3x)

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Solve for x to three decimal places: `3^(2x)=4^(1-3x)` :

Take the logarithm of both sides:

`ln(3^(2x))=ln(4^(1-3x))`   Now use `lna^x=xlna` :

`=> 2xln3=(1-3x)ln4`

`=>2ln(3)x+3ln(4)x=ln4`

`=>x(2ln3+3ln4)=ln4`

`=> x=(ln4)/(2ln3+3ln4)`

`=>x~~0.218104292`

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The solution is `x~~0.218`

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`3^(2*0.218)=3^(.436)~~1.614450995`

`4^(1-3*.218)=4^(.346)~~1.615521555`

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