Question

Find the value of x. if
$3^{3.5}\times {21}^2\times {42}^{2.5}÷2^{2.5}\times 7^{3.5}=(21{)}^x$

• A. $8$
• B. $10$
• C. $12.5$
• D. $6.5$

Answer 1

The correct option is A $8$

$\Rightarrow \frac{(3{)}^{3.5}\times (3\times 7{)}^2\times (2\times 3\times 7{)}^{2.5}\times 7^{3.5}}{2^{2.5}}=(3\times 7{)}^x$

$\Rightarrow \frac{3^{(3.5+2+2.5)}\times 7^{(2+2.5+3.5)}\times 2^{2.5}}{2^{2.5}}=3^x\times 7^x$

$\Rightarrow 3^8\times 7^8=3^x\times 7^x$

$\Rightarrow x=8$. $\left[A\right]$