Trigonometry Examples

$\log (- 5 x) = \log (10 - 3 x)$

Step 1

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$- 5 x = 10 - 3 x$

Step 2

Solve for $x$ .

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Step 2.1

Move all terms containing $x$ to the left side of the equation.

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Step 2.1.1

Add $3 x$ to both sides of the equation.

$- 5 x + 3 x = 10$

Step 2.1.2

Add $- 5 x$ and $3 x$ .

$- 2 x = 10$

Step 2.2

Divide each term in $- 2 x = 10$ by $- 2$ and simplify.

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Step 2.2.1

Divide each term in $- 2 x = 10$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{- 2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $10$ by $- 2$ .

$x = - 5$