Precalculus Examples

$\log (3) (3 x - 2) = 2$

Step 1

Divide each term in $\log (3) (3 x - 2) = 2$ by $\log (3)$ and simplify.

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Step 1.1

Divide each term in $\log (3) (3 x - 2) = 2$ by $\log (3)$ .

$\frac{\log (3) (3 x - 2)}{\log (3)} = \frac{2}{\log (3)}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $\log (3)$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{\log (3) (3 x - 2)}{\log (3)} = \frac{2}{\log (3)}$

Step 1.2.1.2

Divide $3 x - 2$ by $1$ .

$3 x - 2 = \frac{2}{\log (3)}$

Step 2

Add $2$ to both sides of the equation.

$3 x = \frac{2}{\log (3)} + 2$

Step 3

Divide each term in $3 x = \frac{2}{\log (3)} + 2$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = \frac{2}{\log (3)} + 2$ by $3$ .

$\frac{3 x}{3} = \frac{\frac{2}{\log (3)}}{3} + \frac{2}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\frac{2}{\log (3)}}{3} + \frac{2}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{2}{\log (3)}}{3} + \frac{2}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{2}{\log (3)} \cdot \frac{1}{3} + \frac{2}{3}$

Step 3.3.1.2

Multiply $\frac{2}{\log (3)} \cdot \frac{1}{3}$ .

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Step 3.3.1.2.1

Multiply $\frac{2}{\log (3)}$ by $\frac{1}{3}$ .

$x = \frac{2}{\log (3) \cdot 3} + \frac{2}{3}$

Step 3.3.1.2.2

Reorder $\log (3)$ and $3$ .

$x = \frac{2}{3 \cdot \log (3)} + \frac{2}{3}$

Step 3.3.1.2.3

Simplify $3 \cdot \log (3)$ by moving $3$ inside the logarithm.

$x = \frac{2}{\log (3^{3})} + \frac{2}{3}$

Step 3.3.1.3

Raise $3$ to the power of $3$ .

$x = \frac{2}{\log (27)} + \frac{2}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{\log (27)} + \frac{2}{3}$

Decimal Form:

$x = 2.06393551 \dots$