What is ln(11)+5ln(x)-7ln(y) ?

The solution to ln(11)+5ln(x)-7ln(y) is ln((11x^5)/(y^7))

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simplify ln(11)+5ln(x)-7ln(y)

simplify

ln (11) + 5 ln (x) - 7 ln (y)

ln (\frac{11 x ^{5}}{y ^{7}})

Solution steps

ln (11) + 5 ln (x) - 7 ln (y)

Apply log rule:

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

5 ln (x) = ln (x^{5})

= ln (11) + ln (x^{5}) - 7 ln (y)

Apply log rule:

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

ln (11) + ln (x^{5}) = ln (11 x^{5})

= ln (11 x^{5}) - 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^{5}) - ln (y^{7})

Apply log rule:

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

ln (11 x^{5}) - ln (y^{7}) = ln (\frac{11 x ^{5}}{y ^{7}})

= ln (\frac{11 x ^{5}}{y ^{7}})

- \frac{10}{14} \cdot lo g_{2} (\frac{10}{14}) - \frac{4}{14} \cdot lo g_{2} (\frac{4}{14})

lo g_{10} (\frac{x ^{5} y}{z ^{2}})

lo g_{5} (\frac{3 y - 8}{y})

ln (\frac{x x - 4}{x ^{5} + 7})

3 ln (x) + 5 ln (y)

What is ln(11)+5ln(x)-7ln(y) ?
The solution to ln(11)+5ln(x)-7ln(y) is ln((11x^5)/(y^7))