Solve for $17^{x}$ if $\log _{3}\left((-26)+17^{x}\right)=3$.
\[
17^{x}=
\]

Answer

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Answer

Finally, we simplify to get $17^{x}=\boxed{53}$.

Steps

Step 1 ：First, we rewrite the equation using the property of logarithms, which states that $\log _{b} a^{n}=n \log _{b} a$. So, we have $\log _{3}(-26+17^{x})=3$.

Step 2 ：Next, we convert the logarithmic equation to an exponential equation. This gives us $3^{3}=-26+17^{x}$.

Step 3 ：Solving for $17^{x}$, we get $17^{x}=3^{3}+26$.

Step 4 ：Substituting the values, we get $17^{x}=27+26$.

Step 5 ：Finally, we simplify to get $17^{x}=\boxed{53}$.

Solve for $17^{x}$ if $\log _{3}\left((-26)+17^{x}\right)=3$.\[17^{x}=\]

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Solve for $17^{x}$ if $\log _{3}\left((-26)+17^{x}\right)=3$.
\[
17^{x}=
\]