ANSWER
No solution
EXPLANATION
We want to find the solution to the equation given:
[tex]3(5)^{2x}+10=9[/tex]
First, subtract 10 from both sides of the equation:
[tex]\begin{gathered} 3(5)^{2x}+10-10=9-10 \\ 3(5)^{2x}=-1 \end{gathered}[/tex]
Next, divide both sides by 3:
[tex]\begin{gathered} \frac{3}{3}(5)^{2x}=\frac{-1}{3} \\ 5^{2x}=\frac{-1}{3} \end{gathered}[/tex]
Now, convert from an exponential equation to a logarithmic equation as follows:
[tex]\begin{gathered} x^a=b \\ \Rightarrow\log _xb=a \end{gathered}[/tex]
Therefore, we have that:
[tex]\log _5(-\frac{1}{3})=2x[/tex]
Since the logarithm of a negative number cannot be mathematically found, we can conclude that there is no solution for x which satisfies the given equation.
