Root3^x=3^7then find the value of x
Answers
Answered by
0
Answer:
the value of the bases are equal x=7
Answered by
0
Answer:
The value of x is 14.
Step-by-step explanation:
We are given the following in the question:
(\sqrt{3})^x = 3 ^7(
3
)
x
=3
7
We have to find the value of x.
Exponential Properties:
\begin{lgathered}(x^a)^b = x^{ab}\\x^a = x^b \Rightarrow a = b\end{lgathered}
(x
a
)
b
=x
ab
x
a
=x
b
⇒a=b
Solving, we get,
\begin{lgathered}(\sqrt{3})^x = 3 ^7\\(3^{\frac{1}{2}})^x = 3^7\\3^{\frac{x}{2}} = 3^7\\\\\dfrac{x}{2} = 7\\\\x = 14\end{lgathered}
(
3
)
x
=3
7
(3
2
1
)
x
=3
7
3
2
x
=3
7
2
x
=7
x=14
Thus, the value of x is 14.
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