Solve for x 64^(x-1)=4^((x-1)/3)

$64^{x - 1} = 4^{\frac{(x - 1)}{3}}$

Step 1

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

$4^{3 (x - 1)} = 4^{\frac{x - 1}{3}}$

Step 2

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

$3 (x - 1) = \frac{x - 1}{3}$

Step 3

Solve for $x$ .

Multiply both sides by $3$ .

$3 (x - 1) \cdot 3 = \frac{x - 1}{3} \cdot 3$

Simplify.

Simplify the left side.

Simplify $3 (x - 1) \cdot 3$ .

Apply the distributive property.

$(3 x + 3 \cdot - 1) \cdot 3 = \frac{x - 1}{3} \cdot 3$

Multiply $3$ by $- 1$ .

$(3 x - 3) \cdot 3 = \frac{x - 1}{3} \cdot 3$

Apply the distributive property.

$3 x \cdot 3 - 3 \cdot 3 = \frac{x - 1}{3} \cdot 3$

Multiply.

Multiply $3$ by $3$ .

$9 x - 3 \cdot 3 = \frac{x - 1}{3} \cdot 3$

Multiply $- 3$ by $3$ .

$9 x - 9 = \frac{x - 1}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$9 x - 9 = \frac{x - 1}{3} \cdot 3$

Rewrite the expression.

$9 x - 9 = x - 1$

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$9 x - 9 - x = - 1$

Subtract $x$ from $9 x$ .

$8 x - 9 = - 1$

Move all terms not containing $x$ to the right side of the equation.

Add $9$ to both sides of the equation.

$8 x = - 1 + 9$

Add $- 1$ and $9$ .

$8 x = 8$

Divide each term in $8 x = 8$ by $8$ and simplify.

Divide each term in $8 x = 8$ by $8$ .

$\frac{8 x}{8} = \frac{8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{8}{8}$

Divide $x$ by $1$ .

$x = \frac{8}{8}$

Simplify the right side.

Divide $8$ by $8$ .

$x = 1$

Solve for x 64^(x-1)=4^((x-1)/3)

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