Question

Solve for $x$ in the equation $2^{x+1}=8^x.$

• A. 2
• B. 1
• C. $\frac{3}{2}$
• D. $\frac{1}{2}$

Answer 1

The correct option is D $\frac{1}{2}$

$\text{Given,}{2}^{x+1}=8^x$
$2^{x+1}=(2^3{)}^x$

We know, for any non-zero integer 'a' and any integers m and n,
$(a^m{)}^n=a^{mn}.$

$\Rightarrow 2^{x+1}=2^{3x}$

Since the powers in the LHS and the RHS are equal and the bases are the same, their exponents must also be equal.

$\Rightarrow x+1=3x$
$\Rightarrow 2x=1$
$\Rightarrow x=\frac{1}{2}$