Precalculus Examples

$\log (5 x) = \log (2 x + 9)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$5 x = 2 x + 9$

Step 2

Solve for $x$ .

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Step 2.1

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

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Step 2.1.1

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

$5 x - 2 x = 9$

Step 2.1.2

Subtract $2 x$ from $5 x$ .

$3 x = 9$

Step 2.2

Divide each term in $3 x = 9$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x = 9$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $9$ by $3$ .

$x = 3$