Question:
If $10^{x}=64$, find the value of $10^{\left(\frac{x}{2}+1\right)}$
Solution:
We have,
$10^{x}=64$
Taking square root from both sides, we get
$\sqrt{10^{x}}=\sqrt{64}$
$\Rightarrow\left(10^{x}\right)^{\frac{1}{2}}=8$
$\Rightarrow 10^{\left(\frac{x}{2}\right)}=8$
Multiplying both sides by 10 , we get
$10^{\left(\frac{x}{2}\right)} \times 10=8 \times 10$
$\therefore 10^{\left(\frac{x}{2}+1\right)}=80$
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