Algebra Examples

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

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 $b$ .

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Step 3.1

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

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Step 3.1.1

Subtract $b$ from both sides of the equation.

$3 b - 1 - b = - 3$

Step 3.1.2

Subtract $b$ from $3 b$ .

$2 b - 1 = - 3$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the equation.

$2 b = - 3 + 1$

Step 3.2.2

Add $- 3$ and $1$ .

$2 b = - 2$

Step 3.3

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

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Step 3.3.1

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

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

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

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

Step 3.3.2.1.2

Divide $b$ by $1$ .

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

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 2$ by $2$ .

$b = - 1$