Question

If 10^x = 64, find the value of ${10}^{\left(\frac{x}{2}+1\right)}$.

Answer 1

We have,

${10}^x=64$

Taking square root from both sides, we get

$$\begin{gathered} \sqrt{{10}^x}=\sqrt{64} \\ \Rightarrow {\left({10}^x\right)}^{\frac{1}{2}}=8 \\ \Rightarrow {10}^{\left(\frac{x}{2}\right)}=8 \end{gathered}$$

Multiplying both sides by 10, we get

$$\begin{gathered} {10}^{\left(\frac{x}{2}\right)}\times 10=8\times 10 \\ \therefore {10}^{\left(\frac{x}{2}+1\right)}=80 \end{gathered}$$