Question

solve the exponential equation by using the property that $b^x = b^y$ implies $x = y$, for $b > 0$ and $b \
eq 1$..
$6^{-x} = 36$

the solution set is .

Explanation:

Step1: Express 36 as a power of 6

We know that \( 36 = 6^2 \), so we can rewrite the equation \( 6^{-x}=36 \) as \( 6^{-x}=6^2 \).

Step2: Apply the exponential property

Using the property that if \( b^x = b^y \) (where \( b>0 \) and \( b
eq1 \)), then \( x = y \). Here, \( b = 6 \), so we set the exponents equal: \( -x=2 \).

Step3: Solve for x

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

Answer:

\(\{-2\}\)