Question

if 5 to the power 3n divided by 25 is 125 find the value of n​

Answer 1

$\large \green{\bf \:  Given \: Question :- }$

$\bf \:\dfrac{ {5}^{3n} }{25} = 125, \: find \: n.$

$\large \red{AηsωeR :} ✍$

$\large \purple{\sf \: Given :- } ✍$

$\bf \:\dfrac{ {5}^{3n} }{25} = 125$

$\large \green{\sf \:  To  \: Find :- } ✍$

• The value of n.

$\large \blue{\bf \:  Identity \: Used :- } ✍$

$\begin{gathered}(1)\:{\underline{\boxed{\bf{\blue{a^m\times{a^n}\:=\:a^{m\:+\:n}\:}}}}} \\ \end{gathered}</p><p>$

$\begin{gathered}(2)\:{\underline{\boxed{\bf{\purple{\dfrac{a^m}{a^n}\:=\:a^{m\:-\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(3)\:{\underline{\boxed{\bf{\orange{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(4)\:{\underline{\boxed{\bf{\color{peru}{(a^m)^n\:=\:a^{m\times{n}}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(5)\:{\underline{\boxed{\bf{\green{a^m = {a^n} \}\:⟼m \: = n}}}}} \\ \end{gathered}</p><p>$

$\begin{gathered}\Large{\bold{\purple{\underline{CaLcUlAtIoN\::}}}} \\ \end{gathered}$

$\bf \:\dfrac{ {5}^{3n} }{25} = 125$

$\bf \:⟼\dfrac{ {5}^{3n} }{ {5}^{2} } = {5}^{3}$

$\bf \:  ⟼ {5}^{3n - 2} = {5}^{3}$

$\bf \:  ⟼ 3n - 2 = 3$

$\bf \:  ⟼ 3n = 3 + 2$

$\bf \:  ⟼ 3n = 5$

$\bf \:  ⟼ n = \dfrac{5}{3}$

$\large{\boxed{\boxed{\bf{Hence, value \: of \: n = \dfrac{5}{3} }}}}$

Answer 2

Step-by-step explanation:

AηsωeR: ✍

\large \purple{\sf \: Given :- } ✍ Given:− ✍

\bf \:\dfrac{ {5}^{3n} }{25} = 125

25

5

3n

=125

\large \green{\sf \: To \: Find :- } ✍ To Find:− ✍

The value of n.

\large \blue{\bf \: Identity \: Used :- } ✍ IdentityUsed:− ✍

\begin{gathered}\begin{gathered}(1)\:{\underline{\boxed{\bf{\blue{a^m\times{a^n}\:=\:a^{m\:+\:n}\:}}}}} \\ \end{gathered} < /p > < p > \end{gathered}

(1)

a

m

×a

n

=a

m+n

</p><p>

\begin{gathered}\begin{gathered}(2)\:{\underline{\boxed{\bf{\purple{\dfrac{a^m}{a^n}\:=\:a^{m\:-\:n}\:}}}}} \\ \end{gathered}\end{gathered}

(2)

a

n

a

m

=a

m−n

\begin{gathered}\begin{gathered}(3)\:{\underline{\boxed{\bf{\orange{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}\end{gathered}

(3)

x

n

1

=x

−n

\begin{gathered}\begin{gathered}(4)\:{\underline{\boxed{\bf{\color{peru}{(a^m)^n\:=\:a^{m\times{n}}\:}}}}} \\ \end{gathered}\end{gathered}

(4)

(a

m

)

n

=a

m×n

\begin{gathered}\begin{gathered}(5)\:{\underline{\boxed{\bf{\green{a^m = {a^n} \}\:⟼m \: = n}}}}} \\ \end{gathered} < /p > < p > \end{gathered}

(5)

a

m

=a

n

}⟼m=n

</p><p>

\begin{gathered}\begin{gathered}\Large{\bold{\purple{\underline{CaLcUlAtIoN\::}}}} \\ \end{gathered}\end{gathered}

CaLcUlAtIoN:

\bf \:\dfrac{ {5}^{3n} }{25} = 125

25

5

3n

=125

\bf \:⟼\dfrac{ {5}^{3n} }{ {5}^{2} } = {5}^{3}⟼

5

2

5

3n

=5

3

\bf \: ⟼ {5}^{3n - 2} = {5}^{3} ⟼5

3n−2

=5

3

\bf \: ⟼ 3n - 2 = 3 ⟼3n−2=3

\bf \: ⟼ 3n = 3 + 2 ⟼3n=3+2

\bf \: ⟼ 3n = 5 ⟼3n=5

\bf \: ⟼ n = \dfrac{5}{3} ⟼n=

3

5

\large{\boxed{\boxed{\bf{Hence, value \: of \: n = \dfrac{5}{3} }}}}

Hence,valueofn=

3

5