Precalculus Examples

$6^{- 2 x} = 6^{2 - 3 x}$

Step 1

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

$6^{- 2 x} = 6^{2 - 3 x}$

Step 2

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

$- 2 x = 2 - 3 x$

Step 3

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

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Step 3.1

Add $3 x$ to both sides of the equation.

$- 2 x + 3 x = 2$

Step 3.2

Add $- 2 x$ and $3 x$ .

$x = 2$