Student Question

`36^(5x+2)=(1/6)^(11-x)` Solve the equation.

Expert Answers

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To evaluate the given equation `36^(5x+2)=(1/6)^(11-x)` , we may apply `36=6^2`  and  `1/6=6^(-1)` . The equation becomes:


Apply Law of Exponents: `(x^n)^m = x^(n*m)` .



Apply the theorem: If `b^x=b^y` then `x=y` , we get:


Subtract `x` from both sides of the equation.



Subtract 4 from both sides of the equation.



Divide both sides by `9` .





Checking: Plug-in `x=-5/3` on `36^(5x+2)=(1/6)^(11-x)` .







`6^(-38/3)=6^(-38/3) `         TRUE

Final answer:

There is no extraneous solution. The `x=-5/3` is the real exact solution of the equation `36^(5x+2)=(1/6)^(11-x)` . 

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