Trigonometry Examples

$\log_{4} (5 x - 8) = 1$

Step 1

Rewrite $\log_{4} (5 x - 8) = 1$ 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 $b^{y} = x$ .

$4^{1} = 5 x - 8$

Step 2

Solve for $x$ .

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Step 2.1

Rewrite the equation as $5 x - 8 = 4^{1}$ .

$5 x - 8 = 4$

Step 2.2

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

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Step 2.2.1

Add $8$ to both sides of the equation.

$5 x = 4 + 8$

Step 2.2.2

Add $4$ and $8$ .

$5 x = 12$

Step 2.3

Divide each term in $5 x = 12$ by $5$ and simplify.

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Step 2.3.1

Divide each term in $5 x = 12$ by $5$ .

$\frac{5 x}{5} = \frac{12}{5}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $5$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{12}{5}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12}{5}$

Decimal Form:

$x = 2.4$

Mixed Number Form:

$x = 2 \frac{2}{5}$