What is ln(x)-ln(sqrt((y/x)^2+1)+y/x) ?

The solution to ln(x)-ln(sqrt((y/x)^2+1)+y/x) is ln(sqrt(x^2+y^2)-y)

Popular >

simplify ln(x)-ln(sqrt((y/x)^2+1)+y/x)

simplify

ln (x) - ln ((\frac{y}{x})^{2} + 1 + \frac{y}{x})

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

Solution steps

ln (x) - ln ((\frac{y}{x})^{2} + 1 + \frac{y}{x})

Apply log rule:

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

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

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

Simplify

\frac{x}{( \frac{y}{x} ) ^{2} + 1 + \frac{y}{x}} : x^{2} + y^{2} - y

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

lo g_{10} (in f ini t y)

lo g_{4} (\frac{64}{x + 6})

lo g_{2} (4 x) - lo g_{4} (4 x) + lo g_{8} (4 x)

\frac{1}{2} lo g_{2} (9 x^{16}) - \frac{2}{3} lo g_{2} (8 x^{3})

3 ln (x + 7) - ln (x)

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