Question

solve for x.
$16^{-x + 3} = 32$
$x = $

Explanation:

Step1: Express bases as powers of 2

Since \(16 = 2^4\) and \(32 = 2^5\), rewrite the equation:
\((2^4)^{-x + 3}=2^5\)

Step2: Apply exponent rule \((a^m)^n=a^{mn}\)

Simplify the left - hand side:
\(2^{4(-x + 3)}=2^5\)
\(2^{-4x+12}=2^5\)

Step3: Set exponents equal (since bases are equal)

If \(a^m=a^n\) and \(a>0,a
eq1\), then \(m = n\). So:
\(-4x + 12=5\)

Step4: Solve for x

Subtract 12 from both sides:
\(-4x=5 - 12\)
\(-4x=-7\)
Divide both sides by - 4:
\(x=\frac{7}{4}\)

Answer:

\(\frac{7}{4}\)