Precalculus Examples

$3^{2 x + 3} = 6 (x - 3)$

Step 1

Simplify.

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Step 1.1

Apply the distributive property.

$6 x + 6 \cdot - 3$

Step 1.2

Multiply $6$ by $- 3$ .

$6 x - 18$

Step 1.3

Reduce by cancelling the common factors.

$3^{2 x + 3} = 6 x - 18$

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(3)$ of the right side $(6 x - 18)$ equals the exponent $(2 x + 3)$ .

$\log_{3} (6 x - 18) = 2 x + 3$