MCQ
If $10^\text{x}=64,$ what is the value of $10^{\frac{\text{x}}{2}+1}?$
- A$18$
- B$42$
- ✓$80$
- D$81$
✓
Answer
Correct option: C.
$80$
We have to find the value of $10^{\frac{\text{x}}{2}+1}$ provided $10^\text{x}=64$
So,
$10^{\frac{\text{x}}{2}+1}=10^{\text{x}\times\frac{1}{2}}\times10^1$
$=\sqrt[2]{10^\text{x}}\times10^1$
By substituting $10^\text{x}=64$ we get
$=\sqrt[2]{64}\times10^1$
$=\sqrt[2]{8\times8}\times10$
$=8\times10$
$=80$
Hence the correct choice is $c.$
So,
$10^{\frac{\text{x}}{2}+1}=10^{\text{x}\times\frac{1}{2}}\times10^1$
$=\sqrt[2]{10^\text{x}}\times10^1$
By substituting $10^\text{x}=64$ we get
$=\sqrt[2]{64}\times10^1$
$=\sqrt[2]{8\times8}\times10$
$=8\times10$
$=80$
Hence the correct choice is $c.$
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