Algebra Examples

$\log (4 x + 10) = 3$

Step 1

Rewrite $\log (4 x + 10) = 3$ 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 $b^{y} = x$ .

$10^{3} = 4 x + 10$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $4 x + 10 = 10^{3}$ .

$4 x + 10 = 10^{3}$

Step 2.2

Raise $10$ to the power of $3$ .

$4 x + 10 = 1000$

Step 2.3

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

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Step 2.3.1

Subtract $10$ from both sides of the equation.

$4 x = 1000 - 10$

Step 2.3.2

Subtract $10$ from $1000$ .

$4 x = 990$

Step 2.4

Divide each term in $4 x = 990$ by $4$ and simplify.

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Step 2.4.1

Divide each term in $4 x = 990$ by $4$ .

$\frac{4 x}{4} = \frac{990}{4}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $4$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{990}{4}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{990}{4}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Cancel the common factor of $990$ and $4$ .

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Step 2.4.3.1.1

Factor $2$ out of $990$ .

$x = \frac{2 (495)}{4}$

Step 2.4.3.1.2

Cancel the common factors.

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Step 2.4.3.1.2.1

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 495}{2 \cdot 2}$

Step 2.4.3.1.2.2

Cancel the common factor.

$x = \frac{2 \cdot 495}{2 \cdot 2}$

Step 2.4.3.1.2.3

Rewrite the expression.

$x = \frac{495}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{495}{2}$

Decimal Form:

$x = 247.5$

Mixed Number Form:

$x = 247 \frac{1}{2}$