Question

If \( 2^{x+6} = 8^{x+1} \), then the value of \( x \) is:

• A. 1
• B. 1.5
• C. 2
• D. 2.5

Hint:

When solving equations with exponents, make sure to express all terms with the same base so you can easily equate the exponents.

Answer 1

The Correct Option is B

We are given the equation: \[ 2^{x+6} = 8^{x+1} \] Step 1: Express 8 as a power of 2: \[ 8 = 2^3 \] So the equation becomes: \[ 2^{x+6} = (2^3)^{x+1} \] Step 2: Simplify the right-hand side: \[ 2^{x+6} = 2^{3(x+1)} \] \[ 2^{x+6} = 2^{3x+3} \] Step 3: Since the bases are the same, we can equate the exponents: \[ x + 6 = 3x + 3 \] Step 4: Solve for \( x \): \[ x + 6 = 3x + 3 \] \[ 6 - 3 = 3x - x \] \[ 3 = 2x \] \[ x = \frac{3}{2} = 1.5 \] Thus, the value of \( x \) is \( 1.5 \).