Algebra Examples

$\log (4 x - 1)$

Step 1

Set $\log (4 x - 1)$ equal to $0$ .

$\log (4 x - 1) = 0$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite $\log (4 x - 1) = 0$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$10^{0} = 4 x - 1$

Step 2.2

Solve for $x$ .

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Step 2.2.1

Rewrite the equation as $4 x - 1 = 10^{0}$ .

$4 x - 1 = 10^{0}$

Step 2.2.2

Anything raised to $0$ is $1$ .

$4 x - 1 = 1$

Step 2.2.3

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

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Step 2.2.3.1

Add $1$ to both sides of the equation.

$4 x = 1 + 1$

Step 2.2.3.2

Add $1$ and $1$ .

$4 x = 2$

Step 2.2.4

Divide each term in $4 x = 2$ by $4$ and simplify.

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Step 2.2.4.1

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Step 2.2.4.2

Simplify the left side.

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Step 2.2.4.2.1

Cancel the common factor of $4$ .

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Step 2.2.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Step 2.2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{2}{4}$

Step 2.2.4.3

Simplify the right side.

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Step 2.2.4.3.1

Cancel the common factor of $2$ and $4$ .

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Step 2.2.4.3.1.1

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Step 2.2.4.3.1.2

Cancel the common factors.

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Step 2.2.4.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.2.4.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.2.4.3.1.2.3

Rewrite the expression.

$x = \frac{1}{2}$

Step 3