10^(3x)+4=9 Solve the equation.

For the given equation 10^(3x)+4 =9 , we may simplify by combining like terms.
Subtract 4 from both sides of the equation.
10^(3x)+4-4 =9-4
10^(3x)=5
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(10^(3x))=ln(5)
3xln(10)=ln(5)
To isolate the x , divide both sides by 3ln(10).
(3xln(10))/(3ln(10))=(ln(5))/(3ln(10))
x=(ln(5))/(3ln(10))
x= (ln(5))/(ln(1000)) or 0.233 (approximated value).
Checking: Plug-in x=0.233 on 10^(3x)+4 =9.
10^(3*0.233)+4 =?9
10^(0.699)+4 =?9
5.00034535+4=?9
9.00034565~~9   TRUE.
Therefore, there is no extraneous solution.
The x=(ln(5))/(3ln(10)) is the real exact solution of the given equation 10^(3x)+4 =9 .