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

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

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

simplify

3 \cdot 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}})

5 ln (\frac{1 - \frac{2}{2}}{1 + \frac{2}{2}})

\frac{1}{4} ln (15)

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

lo g_{3} (\frac{x ^{4}}{y ^{2}})

ln (2 n^{2} + 4 n - 3) - ln (n^{2} + 4 n + 5)

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