Solve for x 8^(x-1)=32^(3x-2)

$8^{x - 1} = 32^{3 x - 2}$

Step 1

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

$2^{3 (x - 1)} = 2^{5 (3 x - 2)}$

Step 2

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

$3 (x - 1) = 5 (3 x - 2)$

Step 3

Solve for $x$ .

Simplify $3 (x - 1)$ .

Rewrite.

$0 + 0 + 3 (x - 1) = 5 (3 x - 2)$

Simplify by adding zeros.

$3 (x - 1) = 5 (3 x - 2)$

Apply the distributive property.

$3 x + 3 \cdot - 1 = 5 (3 x - 2)$

Multiply $3$ by $- 1$ .

$3 x - 3 = 5 (3 x - 2)$

Simplify $5 (3 x - 2)$ .

Apply the distributive property.

$3 x - 3 = 5 (3 x) + 5 \cdot - 2$

Multiply.

Multiply $3$ by $5$ .

$3 x - 3 = 15 x + 5 \cdot - 2$

Multiply $5$ by $- 2$ .

$3 x - 3 = 15 x - 10$

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

Subtract $15 x$ from both sides of the equation.

$3 x - 3 - 15 x = - 10$

Subtract $15 x$ from $3 x$ .

$- 12 x - 3 = - 10$

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

Add $3$ to both sides of the equation.

$- 12 x = - 10 + 3$

Add $- 10$ and $3$ .

$- 12 x = - 7$

Divide each term in $- 12 x = - 7$ by $- 12$ and simplify.

Divide each term in $- 12 x = - 7$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{- 7}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{- 7}{- 12}$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 12}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{7}{12}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{12}$

Decimal Form:

$x = 0.58\overline{3}$

Solve for x 8^(x-1)=32^(3x-2)

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