2⁵ˣ⁺¹ - 2⁵ˣ = 32
2⁵ˣ.(2 - 1) = 2⁵
2⁵ˣ = 2⁵
5x = 5
x = 5 : 5
x = 1
\(2^{5x+1}-2^{5x}=32\)
\(\Rightarrow2^{5x+1}-2^{5x}=2^5\)
\(\Rightarrow2^{5x}\cdot2-2^{5x}\cdot1=2^5\)
\(\Rightarrow2^{5x}\cdot\left(2-1\right)=2^5\)
\(\Rightarrow2^{5x}\cdot1=2^5\)
\(\Rightarrow2^{5x}=2^5\)
\(\Rightarrow5x=5\)
\(\Rightarrow x=\dfrac{5}{5}\)
\(\Rightarrow x=1\)
25x+1−25x=3225�+1−25�=32
⇒25x+1−25x=25⇒25�+1−25�=25
⇒25x⋅2−25x⋅1=25⇒25�⋅2−25�⋅1=25
⇒25x⋅(2−1)=25⇒25�⋅(2−1)=25
⇒25x⋅1=25⇒25�⋅1=25
⇒25x=25⇒25�=25
⇒5x=5⇒5�=5
2⁵ˣ⁺¹ - 2⁵ˣ = 32
2⁵ˣ.(2 - 1) = 2⁵
2⁵ˣ = 2⁵
5x = 5
x = 5 : 5
x = 1