What is 2ln(1+u)+ln(x)-ln(u) ?

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

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simplify 2ln(1+u)+ln(x)-ln(u)

simplify

2 ln (1 + u) + ln (x) - ln (u)

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

Solution steps

2 ln (1 + u) + ln (x) - ln (u)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (u + 1) = ln ((u + 1)^{2})

= ln ((u + 1)^{2}) + ln (x) - ln (u)

Apply log rule:

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

ln ((1 + u)^{2}) + ln (x) = ln (x (u + 1)^{2})

= ln ((1 + u)^{2} x) - ln (u)

Apply log rule:

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

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

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

- ln (y + 1) - ln (x)

ln (\frac{469}{94.5})

ln (- 2 e^{x})

ln (e^{4 x} arctan (x^{2}))

ln (4) + 3 ln (3)

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