Question

Find the value of x if root find the value of x if root 3 to the power x is equal to 3 to the power 7 3 to the power x is equal to 3 to the power 7 Find the value of x if root 3 to the power x =

Answer 1

Answer:

x=14

Step-by-step explanation:

(Root3)^x=3^7

(Root3)^x=((Root3)^2)^7

(Root3)^x=(Root3)^14

Therefore x=14

Answer 2

The value of x is 14.

Step-by-step explanation:

We are given the following in the question:

$(\sqrt{3})^x = 3 ^7$

We have to find the value of x.

Exponential Properties:

$(x^a)^b = x^{ab}\\x^a = x^b \Rightarrow a = b$

Solving, we get,

$(\sqrt{3})^x = 3 ^7\\(3^{\frac{1}{2}})^x = 3^7\\3^{\frac{x}{2}} = 3^7\\\\\dfrac{x}{2} = 7\\\\x = 14$

Thus, the value of x is 14.

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