Solve open parentheses square root of 7 close parentheses to the 6 x power = 49^{x - 6}.

Solution:

Given, open parentheses square root of 7 close parentheses to the 6 x power = 49x - 6.

We have to solve the given equation.

open parentheses square root of 7 close parentheses to the 6 x power = {√7}^6x

So, \([(7)^{\frac{1}{2}}]^{6x}=49^{(x-6)}\)

Transforming the two sides of the equation to have equal bases.

\([(7)^{\frac{1}{2}}]^{6x}=((7)^{2})^{(x-6)}\)

\((7)^{3x}=(7)^{(2x-12)}\)

On simplification,

3x = 2x - 12

3x - 2x = 12

x = 12

Therefore, the value of x is 12.

Solve open parentheses square root of 7 close parentheses to the 6 x power = 49x - 6.

Summary:

Solving open parentheses square root of 7 close parentheses to the 6 x power = 49x - 6, the value of x is 12.