Question

question
solve for x:
\\(36^{x + 1} = 1296^{x - 4}\\)
answer attempt 1 out of 2
\\(x = \\)

Explanation:

Step1: Express bases as powers of 6

Note that \(36 = 6^2\) and \(1296 = 6^4\). So rewrite the equation:
\((6^2)^{x + 1} = (6^4)^{x - 4}\)

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

Simplify both sides:
\(6^{2(x + 1)} = 6^{4(x - 4)}\)

Step3: Set exponents equal (since bases are equal and positive)

Since \(6^a=6^b\) implies \(a = b\), we have:
\(2(x + 1)=4(x - 4)\)

Step4: Expand both sides

\(2x + 2 = 4x - 16\)

Step5: Solve for \(x\) (subtract \(2x\), add 16)

Subtract \(2x\) from both sides:
\(2 = 2x - 16\)
Add 16 to both sides:
\(18 = 2x\)
Divide by 2:
\(x = 9\)

Answer:

\(x = 9\)