Precalculus Examples

$5^{3 x} = 5^{4 x - 2}$

Step 1

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

$5^{3 x} = 5^{4 x - 2}$

Step 2

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

$3 x = 4 x - 2$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $4 x$ from both sides of the equation.

$3 x - 4 x = - 2$

Step 3.1.2

Subtract $4 x$ from $3 x$ .

$- x = - 2$

Step 3.2

Divide each term in $- x = - 2$ by $- 1$ and simplify.

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Step 3.2.1

Divide each term in $- x = - 2$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 2}{- 1}$

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.

$\frac{x}{1} = \frac{- 2}{- 1}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 2}{- 1}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 2$ by $- 1$ .

$x = 2$