find the value of x so that 1(3/4) *-9 ×(3/4) *-7×(3/4) *4x
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Answer:
Given:
(\dfrac{3}{4})^9{\times}(\dfrac{3}{4})^{-7}=(\dfrac{3}{4})^{4x}(
4
3
)
9
×(
4
3
)
−7
=(
4
3
)
4x
\textbf{To find:}To find:
\text{The value of x}The value of x
\textbf{Solution:}Solution:
\text{Consider,}Consider,
(\dfrac{3}{4})^9{\times}(\dfrac{3}{4})^{-7}=(\dfrac{3}{4})^{4x}(
4
3
)
9
×(
4
3
)
−7
=(
4
3
)
4x
\text{Using,}Using,
\boxed{\bf\,a^m{\times}a^n=a^{m+n}}
a
m
×a
n
=a
m+n
(\dfrac{3}{4})^{9+(-7)}=(\dfrac{3}{4})^{4x}(
4
3
)
9+(−7)
=(
4
3
)
4x
(\dfrac{3}{4})^{2}=(\dfrac{3}{4})^{4x}(
4
3
)
2
=(
4
3
)
4x
\text{Equating powers on bothsides, we get}Equating powers on bothsides, we get
4x=24x=2
\implies\,x=\dfrac{2}{4}⟹x=
4
2
\implies\boxed{\bf\,x=\dfrac{1}{2}}⟹
x=
2
1
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