Solve for x 3^(4x)=27^(x-3)

$3^{4 x} = 27^{x - 3}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$3^{4 x} = 3^{3 (x - 3)}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$4 x = 3 (x - 3)$

Step 3

Solve for $x$ .

Simplify $3 (x - 3)$ .

Apply the distributive property.

$4 x = 3 x + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$4 x = 3 x - 9$

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$4 x - 3 x = - 9$

Subtract $3 x$ from $4 x$ .

$x = - 9$