What is ln(11)+6ln(x)+6ln(y) ?

The solution to ln(11)+6ln(x)+6ln(y) is ln(11x^6y^6)

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simplify ln(11)+6ln(x)+6ln(y)

simplify

ln (11) + 6 ln (x) + 6 ln (y)

ln (11 x^{6} y^{6})

Solution steps

ln (11) + 6 ln (x) + 6 ln (y)

Apply log rule:

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

6 ln (x) = ln (x^{6})

= ln (11) + ln (x^{6}) + 6 ln (y)

Apply log rule:

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

ln (11) + ln (x^{6}) = ln (11 x^{6})

= ln (11 x^{6}) + 6 ln (y)

Apply log rule:

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

6 ln (y) = ln (y^{6})

= ln (11 x^{6}) + ln (y^{6})

Apply log rule:

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

ln (11 x^{6}) + ln (y^{6}) = ln (11 x^{6} y^{6})

= ln (11 x^{6} y^{6})

lo g_{10} (x - 2) + lo g_{10} (x + 1)

lo g_{10} (\frac{4 x}{5})

lo g_{3} (5) + lo g_{3} (10)

ln (\frac{e ^{9}}{5})

lo g_{3} (6 c) + lo g_{3} (\frac{1}{12})

What is ln(11)+6ln(x)+6ln(y) ?
The solution to ln(11)+6ln(x)+6ln(y) is ln(11x^6y^6)