Solve for $x$
\[
27=9^{x+5}
\]

Answer

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Answer

$\boxed{x = -3.5}$ is the solution to the equation $27=9^{x+5}$

Steps

Step 1 ：$27 = 9^{x+5}$ can be rewritten as $3^3 = (3^2)^{x+5}$

Step 2 ：Simplify the equation to $3^3 = 3^{2x+10}$

Step 3 ：Set the exponents equal to each other to get $3 = 2x + 10$

Step 4 ：Solve for $x$ to get $x = -\frac{7}{2}$ or $x = -3.5$

Step 5 ：Check the solution by substituting $x = -3.5$ back into the original equation to get $27 = 9^{-3.5 + 5} = 9^{1.5} = 27$, which is true

Step 6 ：$\boxed{x = -3.5}$ is the solution to the equation $27=9^{x+5}$