Solve for x log base 20 of -2x+7 = log base 20 of 2x-1

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Trigonometry

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

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

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

Solve for $x$ .

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

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

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

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

$- 4 x + 7 = - 1$

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

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Subtract $7$ from both sides of the equation.

$- 4 x = - 1 - 7$

Subtract $7$ from $- 1$ .

$- 4 x = - 8$

Divide each term by $- 4$ and simplify.

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

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

Cancel the common factor of $- 4$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $- 8$ by $- 4$ .

$x = 2$

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