What is ln(x)-ln(y)+2ln(2x-3) ?

The solution to ln(x)-ln(y)+2ln(2x-3) is ln((x(2x-3)^2)/y)

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simplify ln(x)-ln(y)+2ln(2x-3)

simplify

ln (x) - ln (y) + 2 ln (2 x - 3)

ln (\frac{x ( 2 x - 3 ) ^{2}}{y})

Solution steps

ln (x) - ln (y) + 2 ln (2 x - 3)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x) - ln (y) = ln (\frac{x}{y})

= ln (\frac{x}{y}) + 2 ln (2 x - 3)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (2 x - 3) = ln ((2 x - 3)^{2})

= ln (\frac{x}{y}) + ln ((2 x - 3)^{2})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{x}{y}) + ln ((2 x - 3)^{2}) = ln (\frac{x}{y} (2 x - 3)^{2})

= ln (\frac{x}{y} (2 x - 3)^{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= ln (\frac{x ( 2 x - 3 ) ^{2}}{y})

\frac{4 π \cdot 1 0 ^{- 7} \cdot 10 0 ^{2}}{4 π} ln (\frac{1}{7})

ln (\frac{b}{x}) - ln (\frac{a}{x})

ln (\frac{a ^{- 2}}{b ^{4} c ^{- 3}})

ln (\frac{y}{2} \cdot e^{- y ∣ x ∣})

ln 1 + e^{8 I n} - ln (3)

What is ln(x)-ln(y)+2ln(2x-3) ?
The solution to ln(x)-ln(y)+2ln(2x-3) is ln((x(2x-3)^2)/y)