Trigonometry Examples

$\log (6) + \log (x - 3) = - 0.5$

Step 1

Simplify the left side.

Tap for more steps...

Step 1.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (6 (x - 3)) = - 0.5$

Step 1.2

Apply the distributive property.

$\log (6 x + 6 \cdot - 3) = - 0.5$

Step 1.3

Multiply $6$ by $- 3$ .

$\log (6 x - 18) = - 0.5$

Step 2

Rewrite $\log (6 x - 18) = - 0.5$ 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 $b^{y} = x$ .

$10^{- 0.5} = 6 x - 18$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Rewrite the equation as $6 x - 18 = 10^{- 0.5}$ .

$6 x - 18 = 10^{- 0.5}$

Step 3.2

Simplify $10^{- 0.5}$ .

Tap for more steps...

Step 3.2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$6 x - 18 = \frac{1}{10^{0.5}}$

Step 3.2.2

Raise $10$ to the power of $0.5$ .

$6 x - 18 = \frac{1}{3.16227766}$

Step 3.2.3

Divide $1$ by $3.16227766$ .

$6 x - 18 = 0.31622776$

Step 3.3

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

Tap for more steps...

Step 3.3.1

Add $18$ to both sides of the equation.

$6 x = 0.31622776 + 18$

Step 3.3.2

Add $0.31622776$ and $18$ .

$6 x = 18.31622776$

Step 3.4

Divide each term in $6 x = 18.31622776$ by $6$ and simplify.

Tap for more steps...

Step 3.4.1

Divide each term in $6 x = 18.31622776$ by $6$ .

$\frac{6 x}{6} = \frac{18.31622776}{6}$

Step 3.4.2

Simplify the left side.

Tap for more steps...

Step 3.4.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 3.4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{18.31622776}{6}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{18.31622776}{6}$

Step 3.4.3

Simplify the right side.

Tap for more steps...

Step 3.4.3.1

Divide $18.31622776$ by $6$ .

$x = 3.05270462$