LOL sorry for the year late response. Answer: The solution of this exponential equation is x = - 9.
First option: - 9 (negative 9)
Solution:
3^(4x)=27^(x-3)
Expressing 27 in the base 3: 27=3^3
3^(4x)=(3^3)^(x-3)
Using: (a^b)^c=a^(b c) on the right side of the equation, with a=3, b=3, and
c=x-3:
3^(4x)=3^[3(x-3)]
If we have this equality, with the same base on both sides of the equation, the exponents must be equals:
4x=3(x-3)
Solving for x: Eliminating the parentheses on the right side of the equation aplying the distributive property:
4x=3x-3(3)
4x=3x-9
Subtracting 3x both sides of the equation:
4x-3x=3x-9-3x
x=-9