Question

tariq wants to solve for x in the equation $8^{x + 1}=16^{2x - 4}$. which of the following answers should he select? (1 point) \\(\boldsymbol{x = \frac{19}{5}}\\) \\(\boldsymbol{x = 1}\\) \\(\boldsymbol{x = 5}\\) \\(\boldsymbol{x = \frac{13}{11}}\\)

Explanation:

Step1: Express bases as powers of 2

Since \(8 = 2^3\) and \(16 = 2^4\), rewrite the equation:
\((2^3)^{x + 1} = (2^4)^{2x - 4}\)

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

Simplify both sides:
\(2^{3(x + 1)} = 2^{4(2x - 4)}\)

Step3: Set exponents equal (since bases are equal)

\(3(x + 1) = 4(2x - 4)\)

Step4: Expand both sides

\(3x + 3 = 8x - 16\)

Step5: Solve for \(x\)

Subtract \(3x\) from both sides: \(3 = 5x - 16\)
Add 16 to both sides: \(19 = 5x\)
Divide by 5: \(x=\frac{19}{5}\)

Answer:

\(x = \frac{19}{5}\) (the first option)