What is (y^2)/(x^2)+ln((x^6)/(y^2)) ?

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

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simplify (y^2)/(x^2)+ln((x^6)/(y^2))

simplify

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

\frac{y ^{2}}{x ^{2}} + + 6 ln (x) - 2 ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{6}) = 6 ln (x)

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

\frac{ln ( 15 ) - ln ( 2 )}{ln ( 1.05 ) - ln ( 1.19 )}

\frac{ln ( 2 + \frac{( 5 i )}{( n )} ) \cdot ( 5 )}{( n )}

ln ((0.5 + \frac{0.044315}{2}) \cdot 1.05)

lo g_{8} (5) + \frac{1}{4} lo g_{8} (x)

3 lo g_{10} (1 - x) - 3 lo g_{10} (y)

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