Math, asked by harshitasihag27, 3 months ago

5 power x+5powerx=750 find x​

Answers

Answered by Anonymous
1

Answer:

Value \: of \: x = 4Valueofx=4

Step-by-step explanation:

\begin{gathered}Given \\5^x+5^{x-1}=750\end{gathered}

Given

5

x

+5

x−1

=750

\implies 5^{x}+\frac{5^{x}}{5}=750⟹5

x

+

5

5

x

=750

\begin{gathered}By \: Exponential \:Law:\\a^{m-n}= \frac{a^{m}}{a^{n}}\end{gathered}

ByExponentialLaw:

a

m−n

=

a

n

a

m

\implies 5^{x}[1+\frac{1}{5}]=750⟹5

x

[1+

5

1

]=750

\implies 5^{x}[\frac{5+1}{5}]=750⟹5

x

[

5

5+1

]=750

\implies 5^{x}\times \frac{6}{5}=750⟹5

x

×

5

6

=750

\implies 5^{x}=750 \times \frac{5}{6}⟹5

x

=750×

6

5

\implies 5^{x}= 125 \times 5 ⟹5

x

=125×5

\implies 5^{x}=5^{3}\times 5⟹5

x

=5

3

×5

\implies 5^{x}=5^{4}⟹5

x

=5

4

\implies x = 4⟹x=4

\begin{gathered}By, Exponential\: Law :\\If \: a^{m}=a^{n}\: then\: m=n\end{gathered}

By,ExponentialLaw:

Ifa

m

=a

n

thenm=n

Therefore,

Value \: of \: x = 4Valueofx=4

•••♪

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