Trigonometry Examples

$\log_{2} (7) = 3 x - 5$

Step 1

Rewrite the equation as $3 x - 5 = \log_{2} (7)$ .

$3 x - 5 = \log_{2} (7)$

Step 2

Add $5$ to both sides of the equation.

$3 x = \log_{2} (7) + 5$

Step 3

Divide each term in $3 x = \log_{2} (7) + 5$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 x = \log_{2} (7) + 5$ by $3$ .

$\frac{3 x}{3} = \frac{\log_{2} (7)}{3} + \frac{5}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{\log_{2} (7)}{3} + \frac{5}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\log_{2} (7)}{3} + \frac{5}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Rewrite $\frac{\log_{2} (7)}{3}$ as $\frac{1}{3} \log_{2} (7)$ .

$x = \frac{1}{3} \log_{2} (7) + \frac{5}{3}$

Step 3.3.1.2

Simplify $\frac{1}{3} \log_{2} (7)$ by moving $\frac{1}{3}$ inside the logarithm.

$x = \log_{2} (7^{\frac{1}{3}}) + \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \log_{2} (7^{\frac{1}{3}}) + \frac{5}{3}$

Decimal Form:

$x = 2.60245164 \dots$