Question

5^2x-1-5^2x-3=5³.24

Answer 1

\(\Leftrightarrow5^{2x-3+2}-5^{2x-3}=5^3.24\)

\(\Leftrightarrow5^2.5^{2x-3}-5^{2x-3}=5^3.24\)

\(\Leftrightarrow24.5^{2x-3}=5^3.24\)

\(\Leftrightarrow5^{2x-3}=5^3\)

\(\Leftrightarrow2x-3=3\)

\(\Leftrightarrow x=3\)

Answer 2

\(\Leftrightarrow5^{2x}\cdot\dfrac{1}{5}-5^{2x}\cdot\dfrac{1}{125}=5^3\cdot24\)

\(\Leftrightarrow5^{2x}=15625\)

=>2x=6

=>x=3

Answer 3

\(5^{2x-1}-5^{2x-3}=5^3.24\)

\(\Rightarrow5^{2x}:5-5^{2x}:125=5^3.24\)

\(\Rightarrow5^3\left(5^{2x}:5-5^{2x}:125\right)=5^6.24\)

\(\Rightarrow5^{2x}.25-5^{2x}=5^6.24\)

\(\Rightarrow5^{2x}\left(25-1\right)=5^6.24\)

\(\Rightarrow5^{2x}.24=5^6.24\)

\(\Rightarrow2x=6\Rightarrow x=3\)