Finite Math Examples

$\log (5 x - 3) = 2$

Step 1

Rewrite $\log (5 x - 3) = 2$ 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 $b^{y} = x$ .

$10^{2} = 5 x - 3$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $5 x - 3 = 10^{2}$ .

$5 x - 3 = 10^{2}$

Step 2.2

Raise $10$ to the power of $2$ .

$5 x - 3 = 100$

Step 2.3

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

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Step 2.3.1

Add $3$ to both sides of the equation.

$5 x = 100 + 3$

Step 2.3.2

Add $100$ and $3$ .

$5 x = 103$

Step 2.4

Divide each term in $5 x = 103$ by $5$ and simplify.

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Step 2.4.1

Divide each term in $5 x = 103$ by $5$ .

$\frac{5 x}{5} = \frac{103}{5}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $5$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{103}{5}$

Step 2.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{103}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{103}{5}$

Decimal Form:

$x = 20.6$

Mixed Number Form:

$x = 20 \frac{3}{5}$