What is 5ln(x+1)+2ln(x^3)-ln(x) ?

The solution to 5ln(x+1)+2ln(x^3)-ln(x) is ln(x^5(x+1)^5)

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simplify 5ln(x+1)+2ln(x^3)-ln(x)

simplify

5 ln (x + 1) + 2 ln (x^{3}) - ln (x)

ln (x^{5} (x + 1)^{5})

Solution steps

5 ln (x + 1) + 2 ln (x^{3}) - ln (x)

Apply log rule:

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

5 ln (x + 1) = ln ((x + 1)^{5})

= ln ((x + 1)^{5}) + 2 ln (x^{3}) - ln (x)

Apply log rule:

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

2 ln (x^{3}) = ln ((x^{3})^{2})

= ln ((x + 1)^{5}) + ln ((x^{3})^{2}) - ln (x)

Apply log rule:

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

ln ((x + 1)^{5}) + ln ((x^{3})^{2}) = ln ((x^{3})^{2} (x + 1)^{5})

= ln ((x^{3})^{2} (x + 1)^{5}) - ln (x)

(x^{3})^{2} = x^{6}

= ln (x^{6} (x + 1)^{5}) - ln (x)

Apply log rule:

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

ln (x^{6} (x + 1)^{5}) - ln (x) = ln (\frac{x ^{6} ( x + 1 ) ^{5}}{x})

= ln (\frac{x ^{6} ( x + 1 ) ^{5}}{x})

Cancel the common factor:

x

= ln (x^{5} (x + 1)^{5})

0.5 lo g_{10} (c) + 5 lo g_{10} (d)

lo g_{2} (\frac{1}{12}) + 3.4387

2 ln (2 x) - 3 ln (3 x)

- x (ln (5) - ln (3))

ln (ln (v)) + ln (y)

What is 5ln(x+1)+2ln(x^3)-ln(x) ?
The solution to 5ln(x+1)+2ln(x^3)-ln(x) is ln(x^5(x+1)^5)