Trigonometry Examples

$5 \log (x - 10) = 15$

Step 1

Divide each term in $5 \log (x - 10) = 15$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 \log (x - 10) = 15$ by $5$ .

$\frac{5 \log (x - 10)}{5} = \frac{15}{5}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 \log (x - 10)}{5} = \frac{15}{5}$

Step 1.2.1.2

Divide $\log (x - 10)$ by $1$ .

$\log (x - 10) = \frac{15}{5}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $15$ by $5$ .

$\log (x - 10) = 3$

Step 2

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

$10^{3} = x - 10$

Step 3

Solve for $x$ .

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Step 3.1

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

$x - 10 = 10^{3}$

Step 3.2

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

$x - 10 = 1000$

Step 3.3

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

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Step 3.3.1

Add $10$ to both sides of the equation.

$x = 1000 + 10$

Step 3.3.2

Add $1000$ and $10$ .

$x = 1010$