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 (25 e^{2} \cdot \frac{1}{36})

f (x) = ln (x^{4}) - ln (x)

lo g_{5} (4) - lo g_{5} (9)

f (m) = lo g_{m} (\frac{67}{83})

f (x) = lo g_{10} (2 x^{- 3})

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)