5 power x+5powerx=750 find x
Answers
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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