7. Solve for x: 81-² ÷729¹-x=9²x
Answers
Answer:
Answer:
Value \: of \:x = 5Valueofx=5
Step-by-step explanation:
\begin{gathered}Given \\\frac{(81)^{-1}}{(729)^{1-x}}=9^{2x}\end{gathered}
Given
(729)
1−x
(81)
−1
=9
2x
\implies \frac{(9^{2})^{-1}}{(9^{3})^{1-x}}=9^{2x}⟹
(9
3
)
1−x
(9
2
)
−1
=9
2x
\implies \frac{9^{2\times (-1)}}{9^{3\times (1-x)}}=9^{2x}⟹
9
3×(1−x)
9
2×(−1)
=9
2x
\begin{gathered} By \: Exponential \:Law,\\(a^{m})^{n}=a^{mn}\end{gathered}
ByExponentialLaw,
(a
m
)
n
=a
mn
\implies \frac{9^{-2}}{9^{3-3x}}=9^{2x}⟹
9
3−3x
9
−2
=9
2x
\implies 9^{-2-(3-3x)}=9^{2x}⟹9
−2−(3−3x)
=9
2x
\begin{gathered} By \: Exponential \:Law,\\\frac{a^{m}}{a^{n}}=a^{m-n}\end{gathered}
ByExponentialLaw,
a
n
a
m
=a
m−n
\implies 9^{-2-3+3x}=9^{2x}⟹9
−2−3+3x
=9
2x
\implies 9^{-5+3x}=9^{2x}⟹9
−5+3x
=9
2x
\implies -5+3x=2x⟹−5+3x=2x
\begin{gathered} By \: Exponential \:Law,\\If\:a^{m}=a^{n}\: then \: m=n\end{gathered}
ByExponentialLaw,
Ifa
m
=a
n
thenm=n
\implies 3x-2x=5⟹3x−2x=5
\implies x = 5⟹x=5
Therefore,
Value \: of \:x = 5Valueofx=5
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