Question

26 x 5^x-1- 5^x-1=125 

 

Answer 1

\(26\cdot5^{x-1}-5^{x-1}=125\)

\(\Rightarrow5^{^{x-1}}\cdot\left(26-1\right)=125\)

\(\Rightarrow5^{x-1}\cdot25=125\)

\(\Rightarrow5^{x-1}=\dfrac{125}{25}\)

\(\Rightarrow5^{x-1}=5\)

\(\Rightarrow x-1=1\)

\(\Rightarrow x=1+1\)

\(\Rightarrow x=2\)

Answer 2

\(\Leftrightarrow5^{x-1}\cdot\left(26-1\right)=125\)

=>\(5^{x-1}=5\)

=>x-1=1

=>x=2