Answer:
Option D is correct.
x = -12
Step-by-step explanation:
Solve: [tex](\sqrt{7})^{6x} = 49^{x-6}[/tex]
We can write 49 as:
[tex]49 = 7 \cdot 7 = 7^2[/tex]
using exponent rules:
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
[tex](a^m)^n = a^{mn}[/tex]
Apply this rules on the given equation:
[tex]((7)^{\frac{1}{2}})^{6x} = (7^2)^{x-6}[/tex]
[tex]7^{\frac{6x}{2}} = 7^{2(x-6)}[/tex]
Simplify:
[tex]7^{3x} =7^{2x-12}[/tex]
On comparing both sides we get;
[tex]3x = 2x-12[/tex]
Subtract 2x from both sides we get;
x = -12
Therefore, the value of x is -12
