What is 3ln(x)+ln(x^4)-ln(x^3e^x) ?

The solution to 3ln(x)+ln(x^4)-ln(x^3e^x) is ln((x^4)/(e^x))

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simplify 3ln(x)+ln(x^4)-ln(x^3e^x)

simplify

3 ln (x) + ln (x^{4}) - ln (x^{3} e^{x})

ln (\frac{x ^{4}}{e ^{x}})

Solution steps

3 ln (x) + ln (x^{4}) - ln (x^{3} e^{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^{4}) - ln (e^{x} x^{3})

Apply log rule:

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

ln (x^{3}) + ln (x^{4}) = ln (x^{4} x^{3})

= ln (x^{4} x^{3}) - ln (e^{x} x^{3})

Simplify

x^{3} x^{4} : x^{7}

= ln (x^{7}) - ln (x^{3} e^{x})

Apply log rule:

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

ln (x^{7}) - ln (e^{x} x^{3}) = ln (\frac{x ^{7}}{e ^{x} x ^{3}})

= ln (\frac{x ^{7}}{x ^{3} e ^{x}})

Simplify

\frac{x ^{7}}{x ^{3} e ^{x}} : \frac{x ^{4}}{e ^{x}}

= ln (\frac{x ^{4}}{e ^{x}})

lo g_{4} (16 x^{4} y^{3})

ln (\frac{L ^{5} M ^{2}}{K})

ln (\frac{( x + 2 ) ^{4} y ^{\frac{1}{3}}}{( w - 1 ) ^{3}})

2 ln (x^{- 2}) - ln (y^{2})

lo g_{4} (x - 1) + lo g_{4} (2 x - 5)

What is 3ln(x)+ln(x^4)-ln(x^3e^x) ?
The solution to 3ln(x)+ln(x^4)-ln(x^3e^x) is ln((x^4)/(e^x))