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

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

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

simplify

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

ln (\frac{3}{x})

Solution steps

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

Cancel the common factor:

x

= ln (\frac{1}{x}) + ln (3)

Apply log rule:

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

ln (\frac{1}{x}) + ln (3) = ln (3 \cdot \frac{1}{x})

= ln (3 \cdot \frac{1}{x})

Simplify

\frac{1}{x} \cdot 3 : \frac{3}{x}

= ln (\frac{3}{x})

8 lo g_{10} (4 x)

ln (3) 2

lo g_{2} (8) - lo g_{2} (X) - lo g_{2} (Y)

lo g_{4} (\frac{3 y}{z})

lo g_{10} (\frac{10 b}{7})