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How do I solve `4 ^(9x-3) = 50`  ?

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monique06 | Valedictorian

Posted June 5, 2013 at 1:10 PM via web

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How do I solve `4 ^(9x-3) = 50`  ?

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Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted June 5, 2013 at 2:13 PM (Answer #1)

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`4^(9x-3)=50`

To solve for x, take the logarithm of both sides.

`ln 4^(9x-3)=ln50`

At the left side of the equation, apply the property` ln a^m=mlna` .

`(9x-3)ln4=ln50`

Next,divide both sides by ln4.

`((9x-3)ln4)/(ln4)=(ln50)/(ln4)`

`9x-3=(ln50)/(ln4)`

Then, add both sides by 3.

`9x-3+3=(ln50)/(ln4)+3`

`9x=(ln50)/(ln4)+3`

`And, divide both sides by 9.`

`(9x)/9=((ln50)/(ln4)+3)/9`

`x=(ln50)/(9ln4)+3/9`

`x=(ln50)/(9ln4)+1/3`

`x=0.6469`

Hence, the solution to the exponential equation is `x=0.6469` .

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