Algebra Examples

$e^{y} = e^{2 y}$

Step 1

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

$e^{y} = e^{2 y}$

Step 2

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

$y = 2 y$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Subtract $2 y$ from both sides of the equation.

$y - 2 y = 0$

Step 3.1.2

Subtract $2 y$ from $y$ .

$- y = 0$

Step 3.2

Divide each term in $- y = 0$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- y = 0$ by $- 1$ .

$\frac{- y}{- 1} = \frac{0}{- 1}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{0}{- 1}$

Step 3.2.2.2

Divide $y$ by $1$ .

$y = \frac{0}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $0$ by $- 1$ .

$y = 0$