Question

question
solve for x:
$32^{x - 5} = 8^{2x + 3}$

Explanation:

Step1: Express bases as powers of 2

Since \(32 = 2^5\) and \(8 = 2^3\), rewrite the equation:
\((2^5)^{x - 5} = (2^3)^{2x + 3}\)

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

Simplify both sides:
\(2^{5(x - 5)} = 2^{3(2x + 3)}\)
\(2^{5x - 25} = 2^{6x + 9}\)

Step3: Set exponents equal (same base)

Since \(a^m=a^n\) implies \(m = n\) for \(a>0,a
eq1\):
\(5x - 25 = 6x + 9\)

Step4: Solve for \(x\)

Subtract \(5x\) from both sides:
\(-25 = x + 9\)
Subtract 9 from both sides:
\(x = -25 - 9\)
\(x = -34\)

Answer:

\(x = -34\)