Precalculus Examples

$\log (2 x + 1) = \log (15)$

Step 1

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

$2 x + 1 = 15$

Step 2

Solve for $x$ .

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Step 2.1

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1.1

Subtract $1$ from both sides of the equation.

$2 x = 15 - 1$

Step 2.1.2

Subtract $1$ from $15$ .

$2 x = 14$

Step 2.2

Divide each term in $2 x = 14$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $14$ by $2$ .

$x = 7$