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

The solution to ln(e^{3x})+ln(x^3)-ln(3x) is ln((e^{3x}x^2)/3)

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

simplify

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

ln (\frac{e ^{3 x} x ^{2}}{3})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Cancel the common factor:

x

= ln (\frac{e ^{3 x} x ^{2}}{3})

ln (\frac{1}{1 + 1})

lo g_{4} (16 x)

ln (5) + 2 ln (x) - 11 ln (x^{2} + 5)

ln (\frac{4}{7})

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

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