What is 3ln(216)+4ln(1/36) ?

The solution to 3ln(216)+4ln(1/36) is ln(6)

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simplify 3ln(216)+4ln(1/36)

simplify

3 ln (216) + 4 ln (\frac{1}{36})

ln (6)

Decimal Notation

1.79175 \dots

Solution steps

3 ln (216) + 4 ln (\frac{1}{36})

Apply log rule:

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

3 ln (216) = ln (21 6^{3})

= ln (21 6^{3}) + 4 ln (\frac{1}{36})

Apply log rule:

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

4 ln (\frac{1}{36}) = ln ((\frac{1}{36})^{4})

= ln (21 6^{3}) + ln ((\frac{1}{36})^{4})

Apply log rule:

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

ln (21 6^{3}) + ln ((\frac{1}{36})^{4}) = ln (21 6^{3} (\frac{1}{36})^{4})

= ln (21 6^{3} (\frac{1}{36})^{4})

21 6^{3} (\frac{1}{36})^{4} = 6

= ln (6)

\frac{1.6}{2} ln (10) - 1.6 ln (3)

2 ln (a) - ln (a^{2} + 1)

ln ((x^{2} + 4) (x - 4))

ln (2) - ln (3) + ln (15)

ln (\frac{v}{2 v})