Solve the equation $5^{x+3}=15625$ for $x$
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Step 1 ：The given equation is \(5^{x+3}=15625\).

Step 2 ：We can solve this equation by taking the logarithm on both sides. The base of the logarithm should be the same as the base of the exponent on the left side of the equation, which is 5 in this case.

Step 3 ：So, we take the base 5 logarithm on both sides of the equation. The equation then simplifies to \(x+3=\log_{5}{15625}\).

Step 4 ：We can then solve for x by subtracting 3 from both sides of the equation, which gives us \(x=\log_{5}{15625}-3\).

Step 5 ：Calculating the value of \(\log_{5}{15625}\) gives us approximately 6.

Step 6 ：Subtracting 3 from 6 gives us 3.

Step 7 ：So, the solution to the equation is \(x=3\).

Step 8 ：Final Answer: \(x=\boxed{3}\)