What is 1/2 (6ln(x)-7ln(y)) ?

The solution to 1/2 (6ln(x)-7ln(y)) is 1/2 ln((x^6)/(y^7))

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simplify 1/2 (6ln(x)-7ln(y))

simplify

\frac{1}{2} (6 ln (x) - 7 ln (y))

\frac{1}{2} ln (\frac{x ^{6}}{y ^{7}})

Solution steps

\frac{1}{2} (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})

= \frac{1}{2} (ln (x^{6}) - 7 ln (y))

Apply log rule:

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

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

= \frac{1}{2} (ln (x^{6}) - ln (y^{7}))

Apply log rule:

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

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

= \frac{1}{2} ln (\frac{x ^{6}}{y ^{7}})

\frac{1}{3} lo g_{c} (x) + 5 lo g_{c} (y) - 3 lo g_{c} (x)

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

2 lo g_{10} (12) - 3 lo g_{10} (6) + 2 lo g_{10} (2)

lo g_{7} ((\frac{x ^{5}}{y})^{5})

ln (x ln (x))

What is 1/2 (6ln(x)-7ln(y)) ?
The solution to 1/2 (6ln(x)-7ln(y)) is 1/2 ln((x^6)/(y^7))