Question

solve the following elementary exponential equation.
16^{-x} = 8
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4 points
x =

Explanation:

Step1: Express bases as powers of 2

Since \(16 = 2^4\) and \(8 = 2^3\), rewrite the equation: \((2^4)^{-x}=2^3\).

Step2: Simplify left - hand side

Using the power - of - a - power rule \((a^m)^n=a^{mn}\), we get \(2^{-4x}=2^3\).

Step3: Set exponents equal

If \(a^m = a^n\) and \(a>0,a
eq1\), then \(m = n\). So, \(-4x = 3\).

Step4: Solve for x

Divide both sides by \(-4\): \(x=-\frac{3}{4}\).

Answer:

\(-\frac{3}{4}\)