Solve for x 3^(6x)=243^(x+1)

$3^{6 x} = 243^{x + 1}$

Step 1

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

$3^{6 x} = 3^{5 (x + 1)}$

Step 2

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

$6 x = 5 (x + 1)$

Step 3

Solve for $x$ .

Simplify $5 (x + 1)$ .

Apply the distributive property.

$6 x = 5 x + 5 \cdot 1$

Multiply $5$ by $1$ .

$6 x = 5 x + 5$

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

Subtract $5 x$ from both sides of the equation.

$6 x - 5 x = 5$

Subtract $5 x$ from $6 x$ .

$x = 5$