Question

If ${10}^x=64,$ find the value of ${10}^{(\frac{x}{2}+3)}$

Answer 1

$\text{We have,}{10}^x=64\text{Taking square root from both sides, we get}{10}^x=64\Rightarrow ({10}^x{)}^{\frac{1}{2}}=8\Rightarrow {10}^{\frac{x}{2}}=8{10}^{\frac{x}{2}}\times {10}^3=8\times {10}^3{10}^{\frac{x}{2}+3}=8\times {10}^3=8000$