Question

If (root 1024)raise to power 3 =8x??
What is the value of x here??
Options:??
A) 5??
B) 15??
C) 10??
D) 2??
With explanation

Answer 1

$$\begin{gathered} {\left(\sqrt{1024}\right)}^3=8^{\mathrm{x}} \\ \Rightarrow {\left(32\right)}^3={\left(2^3\right)}^{\mathrm{x}} \\ \Rightarrow {\left(2^5\right)}^3={\left(2^3\right)}^{\mathrm{x}} \\ \Rightarrow 2^{15}=2^{3\mathrm{x}} \\ \Rightarrow 15=3\mathrm{x} \\ \Rightarrow \mathrm{x}=\frac{15}{3} \\ \Rightarrow \mathrm{x}=5 \end{gathered}$$