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

The solution to ln(x)+ln(y/x+1)+2/(y/x+1)+6 is ln(y+x)+(2x)/(y+x)+6

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simplify ln(x)+ln(y/x+1)+2/(y/x+1)+6

simplify

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

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

Solution steps

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

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} + 6

Simplify

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

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

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

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

ln (x + 7) - 2 ln (x - 3) + ln (7)

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

lo g_{\frac{4 π ( m ^{3} )}{3}} (2 m)

ln (2 (ln (x) - 1))

20 lo g_{10} (\frac{0.05}{4 π \cdot 8 \cdot 1 0 ^{3}}) + 8 + 8

What is ln(x)+ln(y/x+1)+2/(y/x+1)+6 ?
The solution to ln(x)+ln(y/x+1)+2/(y/x+1)+6 is ln(y+x)+(2x)/(y+x)+6