Precalculus Examples

$\log (x) \cdot 4 = 2$

Step 1

Divide each term in $\log (x) \cdot 4 = 2$ by $4$ and simplify.

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Step 1.1

Divide each term in $\log (x) \cdot 4 = 2$ by $4$ .

$\frac{\log (x) \cdot 4}{4} = \frac{2}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{\log (x) \cdot 4}{4} = \frac{2}{4}$

Step 1.2.1.2

Divide $\log (x)$ by $1$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

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

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Step 1.3.1.1

Factor $2$ out of $2$ .

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

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $2$ out of $4$ .

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

Step 1.3.1.2.2

Cancel the common factor.

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

Step 1.3.1.2.3

Rewrite the expression.

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

Step 2

Rewrite $\log (x) = \frac{1}{2}$ 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 $b^{y} = x$ .

$10^{\frac{1}{2}} = x$

Step 3

Rewrite the equation as $x = 10^{\frac{1}{2}}$ .

$x = 10^{\frac{1}{2}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 10^{\frac{1}{2}}$

Decimal Form:

$x = 3.16227766 \dots$