Solve for $x$
\[
25^{x+4}=125
\]
\[
x=
\]

Answer

Expert–verified

Hide Steps

Answer

Final Answer: $x=\boxed{-\frac{5}{2}}$

Steps

Step 1 ：The given equation is $25^{x+4}=125$.

Step 2 ：We can rewrite 25 as $5^2$ and 125 as $5^3$. So, the equation becomes $(5^2)^{x+4}=5^3$.

Step 3 ：Simplifying the equation, we get $5^{2x+8}=5^3$.

Step 4 ：Since the bases are the same, the exponents must be equal. So, we have $2x+8=3$.

Step 5 ：Solving this equation for x, we get $x=-\frac{5}{2}$.

Step 6 ：So, the solution to the equation $25^{x+4}=125$ is $x=-\frac{5}{2}$.

Step 7 ：Final Answer: $x=\boxed{-\frac{5}{2}}$