What is ln(17)-2ln(x)+3ln(y) ?

The solution to ln(17)-2ln(x)+3ln(y) is ln((17y^3)/(x^2))

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simplify ln(17)-2ln(x)+3ln(y)

simplify

ln (17) - 2 ln (x) + 3 ln (y)

ln (\frac{17 y ^{3}}{x ^{2}})

Solution steps

ln (17) - 2 ln (x) + 3 ln (y)

Apply log rule:

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

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

= ln (17) - ln (x^{2}) + 3 ln (y)

Apply log rule:

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

ln (17) - ln (x^{2}) = ln (\frac{17}{x ^{2}})

= ln (\frac{17}{x ^{2}}) + 3 ln (y)

Apply log rule:

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

3 ln (y) = ln (y^{3})

= ln (\frac{17}{x ^{2}}) + ln (y^{3})

Apply log rule:

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

ln (\frac{17}{x ^{2}}) + ln (y^{3}) = ln (\frac{17}{x ^{2}} y^{3})

= ln (\frac{17}{x ^{2}} y^{3})

Multiply fractions:

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

= ln (\frac{17 y ^{3}}{x ^{2}})

\frac{1}{2} (ln (x) - ln (y)) + 3 ln (z)

ln (\frac{15}{22})

ln (\frac{7}{6}) - ln (\frac{5}{6})

ln (x^{4} e^{2 x})

ln (\frac{1}{x ^{y}})

What is ln(17)-2ln(x)+3ln(y) ?
The solution to ln(17)-2ln(x)+3ln(y) is ln((17y^3)/(x^2))