Question

What would be the value of $x$ for the equation $8^x=16$ ?

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{5}{3}$

Answer 1

The correct option is C $\frac{4}{3}$

$8^x=16$
$(2^3{)}^x=2^4\because [(2^3{)}^x=8^x]$ and $[2^4=16]\cdots \left(i\right)$
$2^{3x}=2^4\cdots$ From $\left(i\right)$
Using laws of exponents, as bases are same, we can equate the exponents of the equation
Hence, $2^{3x}=2^4$
$3x=4$
$\therefore x=\frac{4}{3}$