Question

$\text{If}{\left(\sqrt{1024}\right)}^3=8^x\text{, then}x\text{is}$ ________.

• A. 15
• B. 5
• C. 2
• D. 10

Answer 1

The correct option is B

5

Given:
${\left(\sqrt{1024}\right)}^3=8^x$

$\Rightarrow \left(\sqrt{(}{2}^{10}\right){)}^3=8^x$.

$\Rightarrow \left(\sqrt{(}\right(2^5{)}^2){)}^3=8^x$. {as ${\left(a^m\right)}^n$=$a^{mn}$}

${\Rightarrow \left(2^5\right)}^3={\left(2^3\right)}^x$

${\Rightarrow \left(2^3\right)}^5={\left(2^3\right)}^x$

$\Rightarrow (8{)}^5$= $(8{)}^x$

We know that, if $a^n$= $a^m$ then, $n=m$.

Hence,
$\Rightarrow x=5$