What is ln(2)+5ln(x)-7ln(y) ?

The solution to ln(2)+5ln(x)-7ln(y) is ln((2x^5)/(y^7))

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simplify ln(2)+5ln(x)-7ln(y)

simplify

ln (2) + 5 ln (x) - 7 ln (y)

ln (\frac{2 x ^{5}}{y ^{7}})

Solution steps

ln (2) + 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 (2) + ln (x^{5}) - 7 ln (y)

Apply log rule:

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

ln (2) + ln (x^{5}) = ln (2 x^{5})

= ln (2 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 (2 x^{5}) - ln (y^{7})

Apply log rule:

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

ln (2 x^{5}) - ln (y^{7}) = ln (\frac{2 x ^{5}}{y ^{7}})

= ln (\frac{2 x ^{5}}{y ^{7}})

3 lo g_{c} (x) - \frac{1}{2} lo g_{c} (y) + 4 lo g_{c} (w)

lo g_{10} (2) + lo g_{10} (125)

ln ((8 x)^{\frac{1}{2}}) + ln (4) x^{2} - ln ((16 x)^{\frac{1}{2}})

lo g_{10} (\frac{x + y}{z})

ln (\frac{2 x ^{3}}{( x + 4 ) ^{2}})

What is ln(2)+5ln(x)-7ln(y) ?
The solution to ln(2)+5ln(x)-7ln(y) is ln((2x^5)/(y^7))