Trigonometry Examples

$\log_{20} (- 2 x + 7) = \log_{20} (2 x - 1)$

Step 1

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

$- 2 x + 7 = 2 x - 1$

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

Subtract $2 x$ from both sides of the equation.

$- 2 x + 7 - 2 x = - 1$

Step 2.1.2

Subtract $2 x$ from $- 2 x$ .

$- 4 x + 7 = - 1$

Step 2.2

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

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Step 2.2.1

Subtract $7$ from both sides of the equation.

$- 4 x = - 1 - 7$

Step 2.2.2

Subtract $7$ from $- 1$ .

$- 4 x = - 8$

Step 2.3

Divide each term in $- 4 x = - 8$ by $- 4$ and simplify.

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Step 2.3.1

Divide each term in $- 4 x = - 8$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 8}{- 4}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 4$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 8}{- 4}$

Step 2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 4}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $- 8$ by $- 4$ .

$x = 2$