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

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

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simplify ln(x)+ln(y/x+1)+2/(y/x+1)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

x (\frac{y}{x} + 1) : y + x

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

\frac{2}{\frac{y}{x} + 1} = \frac{2 x}{y + x}

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

ln (\frac{y}{e})

lo g_{10} (\frac{( x - 5 ) ^{2}}{x ^{5}})

3 ln (10) - ln (8)

ln (\frac{40}{7})

ln (\frac{4}{3} x^{2})

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