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

The solution to 2(ln(x)+ln(3))-3ln(y) is ln((9x^2)/(y^3))

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

simplify

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

ln (\frac{9 x ^{2}}{y ^{3}})

Solution steps

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

Apply log rule:

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

ln (x) + ln (3) = ln (3 x)

= 2 ln (x \cdot 3) - 3 ln (y)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( x \cdot 3 ) ^{2}}{y ^{3}} : \frac{9 x ^{2}}{y ^{3}}

= ln (\frac{9 x ^{2}}{y ^{3}})

lo g_{3} (x) + lo g_{3} (5 y)

3 lo g_{2} (a) + 5 lo g_{2} (b)

ln (13 x)

\frac{2}{5} lo g_{10} (m) + 4 lo g_{10} (n)

ln (\frac{3 ^{x} 6 ^{2 x}}{2 ^{3 x}})

What is 2(ln(x)+ln(3))-3ln(y) ?
The solution to 2(ln(x)+ln(3))-3ln(y) is ln((9x^2)/(y^3))