What is 5ln(u)-2ln(6) ?

The solution to 5ln(u)-2ln(6) is ln((u^5)/(36))

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simplify 5ln(u)-2ln(6)

simplify

5 ln (u) - 2 ln (6)

ln (\frac{u ^{5}}{36})

Solution steps

5 ln (u) - 2 ln (6)

Apply log rule:

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

5 ln (u) = ln (u^{5})

= ln (u^{5}) - 2 ln (6)

Apply log rule:

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

2 ln (6) = ln (6^{2})

= ln (u^{5}) - ln (6^{2})

Apply log rule:

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

ln (u^{5}) - ln (6^{2}) = ln (\frac{u ^{5}}{6 ^{2}})

= ln (\frac{u ^{5}}{6 ^{2}})

6^{2} = 36

= ln (\frac{u ^{5}}{36})

lo g_{4} (5) + lo g_{4} (16) + lo g_{4} (1.25)

ln (\frac{25.65}{95})

lo g_{5} (3 x^{2}) + ln (4 x^{3})

\frac{1}{11.81 \cdot 1 0 ^{- 4}} ln (\frac{1.3}{0.02})

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