Answered

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


x = negative 21 over 2

x = −6

x = negative 6 over 5

x = −12

Verified Answer :

bireland203

The equation is not setup properly, possibly it is your teacher's fault.

From external research, I would say the answer is x = -12.

Answer:

Option D is correct.

x = -12

Step-by-step explanation:

Solve:  \((\sqrt{7})^{6x} = 49^{x-6}\)

We can write 49 as:

\(49 = 7 \cdot 7 = 7^2\)

using exponent rules:

\(\sqrt[n]{a^m}=a^{\frac{m}{n}}\)

\((a^m)^n = a^{mn}\)

Apply this rules on the given equation:

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

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

Simplify:

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

On comparing both sides we get;

\(3x = 2x-12\)

Subtract 2x from both sides we get;

x = -12

Therefore, the value of x is -12

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