Solve for b 5^(3b-1)=5^(b-3)

$5^{3 b - 1} = 5^{b - 3}$

Step 1

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

$5^{3 b - 1} = 5^{b - 3}$

Step 2

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

$3 b - 1 = b - 3$

Step 3

Solve for $b$ .

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

Subtract $b$ from both sides of the equation.

$3 b - 1 - b = - 3$

Subtract $b$ from $3 b$ .

$2 b - 1 = - 3$

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

Add $1$ to both sides of the equation.

$2 b = - 3 + 1$

Add $- 3$ and $1$ .

$2 b = - 2$

Divide each term in $2 b = - 2$ by $2$ and simplify.

Divide each term in $2 b = - 2$ by $2$ .

$\frac{2 b}{2} = \frac{- 2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b}{2} = \frac{- 2}{2}$

Divide $b$ by $1$ .

$b = \frac{- 2}{2}$

Simplify the right side.

Divide $- 2$ by $2$ .

$b = - 1$