For what value of x does 34% – 27^x-3?

LOL sorry for the year late response.

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