What is 3ln(x)-(ln(x+1)+ln(x)) ?

The solution to 3ln(x)-(ln(x+1)+ln(x)) is ln((x^2)/(x+1))

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simplify 3ln(x)-(ln(x+1)+ln(x))

simplify

3 ln (x) - (ln (x + 1) + ln (x))

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

Solution steps

3 ln (x) - (ln (x + 1) + ln (x))

Apply log rule:

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

ln (x + 1) + ln (x) = ln (x (x + 1))

= 3 ln (x) - ln ((x + 1) x)

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln (x^{3}) - ln (x (x + 1))

Apply log rule:

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

ln (x^{3}) - ln (x (x + 1)) = ln (\frac{x ^{3}}{x ( x + 1 )})

= ln (\frac{x ^{3}}{( x + 1 ) x})

Cancel the common factor:

x

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

lo g_{7} (\frac{n}{2})

lo g_{10} (28) + 3 lo g_{10} (8 (42)) - 2.92

ln (e (5 x)) + e^{0}

lo g_{e} (x x^{2} + 1)

- 0.6 \cdot lo g_{2} (0.6) - 0.4 \cdot lo g_{2} (0.4)

What is 3ln(x)-(ln(x+1)+ln(x)) ?
The solution to 3ln(x)-(ln(x+1)+ln(x)) is ln((x^2)/(x+1))