Question

solve the exponential equation by using the property that $b^x = b^y$ implies $x = y$, for $b > 0$ and $b \
eq 1$..
$5^{-x} = 25$
the solution set is \boxed{}.

Explanation:

Step1: Express 25 as a power of 5

We know that \(25 = 5^2\), so the equation \(5^{-x}=25\) can be rewritten as \(5^{-x}=5^2\).

Step2: Apply the exponential property

Using the property \(b^x = b^y\) implies \(x = y\) (where \(b = 5>0\) and \(b
eq1\)), we set the exponents equal: \(-x = 2\).

Step3: Solve for x

Multiply both sides by -1 to get \(x=-2\).

Answer:

\(\{-2\}\)