What is 7ln(x)+2ln(3)-5ln(y) ?

The solution to 7ln(x)+2ln(3)-5ln(y) is ln((9x^7)/(y^5))

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simplify 7ln(x)+2ln(3)-5ln(y)

simplify

7 ln (x) + 2 ln (3) - 5 ln (y)

ln (\frac{9 x ^{7}}{y ^{5}})

Solution steps

7 ln (x) + 2 ln (3) - 5 ln (y)

Apply log rule:

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

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

= ln (x^{7}) + 2 ln (3) - 5 ln (y)

Apply log rule:

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

2 ln (3) = ln (3^{2})

= ln (x^{7}) + ln (3^{2}) - 5 ln (y)

Apply log rule:

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

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

= ln (3^{2} x^{7}) - 5 ln (y)

3^{2} = 9

= ln (9 x^{7}) - 5 ln (y)

Apply log rule:

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

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

= ln (9 x^{7}) - ln (y^{5})

Apply log rule:

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

ln (9 x^{7}) - ln (y^{5}) = ln (\frac{9 x ^{7}}{y ^{5}})

= ln (\frac{9 x ^{7}}{y ^{5}})

\frac{1}{3} lo g_{10} (x) - lo g_{10} (5)

3 ln ∣ x ∣ - 2 ln ∣ x + 1 ∣

ln (a^{4} b^{7})

\frac{1}{2} lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

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

What is 7ln(x)+2ln(3)-5ln(y) ?
The solution to 7ln(x)+2ln(3)-5ln(y) is ln((9x^7)/(y^5))