What is ln(11)+6ln(x)-7ln(y) ?

The solution to ln(11)+6ln(x)-7ln(y) is ln((11x^6)/(y^7))

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simplify ln(11)+6ln(x)-7ln(y)

simplify

ln (11) + 6 ln (x) - 7 ln (y)

ln (\frac{11 x ^{6}}{y ^{7}})

Solution steps

ln (11) + 6 ln (x) - 7 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}) - 7 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}) - 7 ln (y)

Apply log rule:

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

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

= ln (11 x^{6}) - ln (y^{7})

Apply log rule:

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

ln (11 x^{6}) - ln (y^{7}) = ln (\frac{11 x ^{6}}{y ^{7}})

= ln (\frac{11 x ^{6}}{y ^{7}})

lo g_{6} (\frac{x ^{3} y}{2 z ^{7}})

- 0.4 + \frac{0.592}{2} \cdot lo g_{10} (\frac{0.2}{1})

\frac{4}{10} lo g_{2} (\frac{10}{4}) + \frac{6}{10} lo g_{2} (\frac{10}{6})

- lo g_{10} (1.1 \cdot 1 0^{- 7})

\frac{1}{4} ln (\frac{38}{13})

What is ln(11)+6ln(x)-7ln(y) ?
The solution to ln(11)+6ln(x)-7ln(y) is ln((11x^6)/(y^7))