find the value of 6(5^x-5^x-1)=120
Answers
Answer:
Appropriate Question :-
If \large\sf{6( {5}^{x} - {5}^{x - 1} ) = 120}6(5x−5x−1)=120 , then find the value of x.
Answer :-
Value of x = 2.
Solution :-
\begin{gathered}\implies\sf{6( {5}^{x} - {5}^{x - 1} ) = 120} \\ \\\end{gathered}⟹6(5x−5x−1)=120
\begin{gathered}\implies\sf{({5}^{x} - {5}^{x} \times {5}^{ - 1} ) = \dfrac{120}{6} } \\ \\\end{gathered}⟹(5x−5x×5−1)=6120
\begin{gathered}\implies\sf{{5}^{x}(1 - {5}^{ - 1} ) = 20} \\ \\\end{gathered}⟹5x(1−5−1)=20
\begin{gathered}\implies\sf{{5}^{x}\bigg(1 - \dfrac{1}{5} \bigg ) = 20} \\ \\\end{gathered}⟹5x(1−51)=20
\begin{gathered}\implies\sf{{5}^{x}\bigg( \dfrac{5 - 1}{5} \bigg ) = 20} \\ \\\end{gathered}⟹5x(55−1)=20
\begin{gathered}\implies\sf{{5}^{x} \times \dfrac{4}{5} = 20} \\ \\\end{gathered}⟹5x×54=20
\begin{gathered}\implies\sf{ {5}^{x} = \dfrac{ 20 \times 5}{4} }\\ \\\end{gathered}⟹5x=420×5
\begin{gathered}\implies\sf{ {5}^{x} = 25}\\ \\\end{gathered}⟹5x=25
\begin{gathered}\implies\sf{ {5}^{x} = {5}^{2} }\\ \\\end{gathered}⟹5x=52
\begin{gathered}\implies\underline{\boxed{\tt\red{ x = 2}}}\\ \\\end{gathered}⟹x=2
Therefore, Value of x = 2.
Answer:
value of x is 2 it is the correct answer