`2^(0.1x)-5=12` Solve the equation.

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For the given equation `2^(0.1x)-5=12` , we may simplify by combining like terms.

Add `5` on both sides of the equation.



Take the "`ln` " on both sides to be able to bring down the exponent value.

Apply the natural logarithm property: `ln(x^n)= n*ln(x)` .




Multiply both sides by `10` .



To isolate `x` , divide both sides by `ln(2)` .


`x=(10ln(17))/(ln(2)) or40.87 ` (approximated value)

Checking: Plug-in `x=40.87`  on `2^(0.1x)-5=12` .




`12=12 `   TRUE

Note: `2^(4.087)=16.99454698~~17`.


Therefore, there is no extraneous solution.

The `x=(10ln(17))/(ln(2))`    is the real exact solution of the given equation `2^(0.1x)-5=12` .

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