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

For the given equation 2^(0.1x)-5=12 , we may simplify by combining like terms.
Add 5 on both sides of the equation.
2^(0.1x)-5+5=12+5
2^(0.1x)=17
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) .
ln(2^(0.1x))=ln(17)
0.1xln(2)=ln(17)
(xln(2))/10=ln(17)
Multiply both sides by 10 .
(xln(2))/10*10=ln(17)*10
xln(2)=10ln(17)
To isolate x , divide both sides by ln(2) .
(xln(2))/(ln(2))=(10ln(17))/(ln(2))
x=(10ln(17))/(ln(2)) or40.87 (approximated value)
Checking: Plug-in x=40.87  on 2^(0.1x)-5=12 .
2^(0.1*40.87)-5=?12
2^(4.087)-5=?12
17-5=?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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