Solve log_(2) (x-3)- log_(2) (x 1)= log_(2) 3- log_(2

Evaluate

lo g_{2} (x - 3) - lo g_{2} (x \times 1) = lo g_{2} (3) - lo g_{2} (7)

Find the domain

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lo g_{2} (x - 3) - lo g_{2} (x \times 1) = lo g_{2} (3) - lo g_{2} (7), x > 3

Simplify

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lo g_{2} (\frac{x - 3}{x}) = lo g_{2} (3) - lo g_{2} (7)

Use the logarithm product rule

lo g_{2} (\frac{x - 3}{x}) = lo g_{2} (\frac{3}{7})

Evaluate the logarithm

\frac{x - 3}{x} = \frac{3}{7}

Cross multiply

(x - 3) \times 7 = x \times 3

Simplify the equation

7 (x - 3) = x \times 3

Simplify the equation

7 (x - 3) = 3 x

Expand the expression

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7 x - 21 = 3 x

Move the variable to the left side

7 x - 21 - 3 x = 0

Subtract the terms

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4 x - 21 = 0

Move the constant to the right side

4 x = 0 + 21

Removing 0 doesn't change the value,so remove it from the expression

4 x = 21

Divide both sides

\frac{4 x}{4} = \frac{21}{4}

Divide the numbers

x = \frac{21}{4}

Check if the solution is in the defined range

x = \frac{21}{4}, x > 3

Solution

x = \frac{21}{4}

Alternative Form

x = 5.25

Solve the equation