Question

Find value of the variable n-(see the pic) ​

Answer 1

Given :-

$\tt{25^n^-^1+100=5^2^n^-^1}$

To find :-

The value of 'n'.

Solution :-

$\tt{25^{n-1}=5^2^{(n-1)}=5^{2n-2}}$

$\displaystyle{\tt{5^{2n-2}+100=5^{2n-1}}}\\\\\displaystyle{\tt{\implies \frac{5^{2n-1}}{5}+100=5^{2n-1}} }\\\\\displaystyle{\texttt{Let }}5^{2n-1}\texttt{ be x.}\\\\\displaystyle{\tt{\implies \frac{x}{5}+100=x }}\\\\\displaystyle{\tt{\implies 100=x-\frac{x}{5} }}\\\\\displaystyle{\tt{\implies 100=\frac{4x}{5} }}\\\\\displaystyle{\tt{\implies x=\frac{500}{4}=125 }}$

$\tt{Now,}\\\\\displaystyle{\tt{5^{2n-1}=125}}\\\\\displaystyle{\tt{\implies 5^{2n-1}=5^3}}\\\\\displaystyle{\tt{\implies 2n-1=3}}\\\\\tt{As\ the\ base\ is\ same\ in\ both\ the\ sides\ i.e.\ 5.}\\\\\displaystyle{\tt{n=\frac{3+1}{2} }}\\\displaystyle{\tt{\boxed{\implies n=2}}}$

Answer 2

Answer:

tt{25^n^-^1+100=5^2^n^-^1}

To find :-

The value of 'n'.

Solution :-

\tt{25^{n-1}=5^2^{(n-1)}=5^{2n-2}}

\begin{gathered}\displaystyle{\tt{5^{2n-2}+100=5^{2n-1}}}\\\\\displaystyle{\tt{\implies \frac{5^{2n-1}}{5}+100=5^{2n-1}} }\\\\\displaystyle{\texttt{Let }}5^{2n-1}\texttt{ be x.}\\\\\displaystyle{\tt{\implies \frac{x}{5}+100=x }}\\\\\displaystyle{\tt{\implies 100=x-\frac{x}{5} }}\\\\\displaystyle{\tt{\implies 100=\frac{4x}{5} }}\\\\\displaystyle{\tt{\implies x=\frac{500}{4}=125 }}\end{gathered}

5

2n−2

+100=5

2n−1

⟹

5

5

2n−1

+100=5

2n−1

Let 5

2n−1

be x.

⟹

5

x

+100=x

⟹100=x−

5

x

⟹100=

5

4x

⟹x=

4

500

=125

\begin{gathered}\tt{Now,}\\\\\displaystyle{\tt{5^{2n-1}=125}}\\\\\displaystyle{\tt{\implies 5^{2n-1}=5^3}}\\\\\displaystyle{\tt{\implies 2n-1=3}}\\\\\tt{As\ the\ base\ is\ same\ in\ both\ the\ sides\ i.e.\ 5.}\\\\\displaystyle{\tt{n=\frac{3+1}{2} }}\\\displaystyle{\tt{\boxed{\implies n=2}}}\\\end{gathered}

Now,

5

2n−1

=125

⟹5

2n−1

=5

3

⟹2n−1=3

As the base is same in both the sides i.e. 5.

n=

2

3+1

⟹n=2

Step-by-step explanation:

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