What is ln(3)+7ln(x)-2ln(y) ?

The solution to ln(3)+7ln(x)-2ln(y) is ln((3x^7)/(y^2))

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simplify ln(3)+7ln(x)-2ln(y)

simplify

ln (3) + 7 ln (x) - 2 ln (y)

ln (\frac{3 x ^{7}}{y ^{2}})

Solution steps

ln (3) + 7 ln (x) - 2 ln (y)

Apply log rule:

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

7 ln (x) = ln (x^{7})

= ln (3) + ln (x^{7}) - 2 ln (y)

Apply log rule:

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

ln (3) + ln (x^{7}) = ln (3 x^{7})

= ln (3 x^{7}) - 2 ln (y)

Apply log rule:

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

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

= ln (3 x^{7}) - ln (y^{2})

Apply log rule:

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

ln (3 x^{7}) - ln (y^{2}) = ln (\frac{3 x ^{7}}{y ^{2}})

= ln (\frac{3 x ^{7}}{y ^{2}})

lo g_{5} (\frac{4 a b ^{3} c ^{4}}{d ^{2}})

lo g_{3} (c) + lo g_{3} (c + 6)

lo g_{2} (6 a^{2} y^{4})

lo g_{3} (c) + lo g_{3} (c + 9)

ln (s t) + ln (\frac{s}{e})

What is ln(3)+7ln(x)-2ln(y) ?
The solution to ln(3)+7ln(x)-2ln(y) is ln((3x^7)/(y^2))