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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- 450 ln (\frac{c}{1.75 b})

ln (\frac{1}{x ( x + 1 ) ( x + 2 )})

- t^{2} + ln (5 t) + 15

ln (\frac{2.527}{2 x + 1}) - 5

ln (\frac{( x + 1 ) ( x + 2 )}{x + 3})

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