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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

lo g_{b} (\frac{x ^{2} y ^{2}}{z ^{2}})

ln (x^{2} \frac{y}{z})

\frac{1}{2} ln (\frac{1 + \frac{1}{2}}{1 - \frac{1}{2}})

ln (3 ab \cdot 5 c)

lo g_{a} (\frac{m}{n})

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