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^{5x - 3} = 25 )
the solution set is (\boxed{quad}).

Explanation:

Step1: Express 25 as a power of 5

We know that \(25 = 5^2\), so rewrite the equation \(5^{5x - 3}=25\) as \(5^{5x - 3}=5^2\).

Step2: Apply the exponential property

Using the property \(b^x = b^y\) implies \(x = y\) (for \(b>0\) and \(b
eq1\)), we set the exponents equal: \(5x - 3 = 2\).

Step3: Solve for x

Add 3 to both sides: \(5x=2 + 3=5\). Then divide both sides by 5: \(x=\frac{5}{5}=1\).

Answer:

\(\{1\}\)