Question

\(\dfrac{2^{2x-3}}{4^{10}}=8^3.16^5\)

Answer 1

\(\dfrac{2^{2x-3}}{4^{10}}=8^3.16^5\)

\(\Rightarrow\dfrac{2^{2x-3}}{\left(2^2\right)10}=\left(2^3\right)^3.\left(2^4\right)^5\)

\(\Rightarrow\dfrac{2^{2x-3}}{2^{20}}=2^9.2^{20}\)

\(\Rightarrow2^{2x-3}:2^{20}=2^{29}\)

\(\Rightarrow2^{2x-3}=2^{49}\)

\(\Rightarrow2x-3=49\)

\(\Rightarrow2x=49+3\)

\(\Rightarrow2x=52\)

`=> x = 52 : 2`

`=> x = 26`

Answer 2

\(\Leftrightarrow2^{2x-3}=2^9\cdot2^{20}\cdot2^{20}=2^{49}\)

=>2x-3=49

=>2x=52

=>x=26