`3(5^(x-1)) = 86` Solve the equation accurate to three decimal places

Problem:`3(5^(x-1))=86`

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To simplify, we divide both sides by 3:

`(3(5^(x-1)))/3=(86)/3`

`5^(x-1)=(86)/3`

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Take the "log" on both sides to apply the logarithm property: `log(x^y)=y*log(x)` .

Applying on the given problem: 

`log(5^(x-1))=log((86)/3)`  ` ` 

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`(x-1)log(5)=log((86)/3)`

Divide both sides by` log(5)`  ` ` to isolate`(x-1)` :

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Add 1 on both sides to solve x:

`x-1=(log((86)/3))/(log(5))`

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 +1                                  +1

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`x=(log((86)/3))/(log(5))+1`

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`x~~3.085`

To check, plug-in`x=3.085` in  ` ` :

`3(5^(3.085-1))=?86`

`3*5^2.085=?86`

`3*28.66503386=?86`

`85.99510157~~86`   TRUE.

 Conclusion:  x= 3.085 as the real solution