What is ln(27)+ln(9)-ln(1/3)*4ln(sqrt(3)) ?

The solution to ln(27)+ln(9)-ln(1/3)*4ln(sqrt(3)) is 5ln(3)+2ln^2(3)

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simplify ln(27)+ln(9)-ln(1/3)*4ln(sqrt(3))

simplify

ln (27) + ln (9) - ln (\frac{1}{3}) \cdot 4 ln (3)

5 ln (3) + 2 ln^{2} (3)

Decimal Notation

7.90695 \dots

Solution steps

ln (27) + ln (9) - ln (\frac{1}{3}) \cdot 4 ln (3)

Apply log rule:

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

ln (27) + ln (9) = ln (27 \cdot 9)

= ln (27 \cdot 9) - 4 ln (3) ln (\frac{1}{3})

Multiply the numbers:

27 \cdot 9 = 243

= ln (243) - ln (\frac{1}{3}) \cdot 4 ln (3)

ln (\frac{1}{3}) \cdot 4 ln (3) = 2 ln (3) ln (\frac{1}{3})

= ln (243) - 2 ln (3) ln (\frac{1}{3})

ln (243) = 5 ln (3)

ln (\frac{1}{3}) ln (3) \cdot 2 = - 2 ln^{2} (3)

= 5 ln (3) - (- 2 ln^{2} (3))

Apply rule

- (- a) = a

= 5 ln (3) + ln^{2} (3) \cdot 2

ln (\frac{2 x ^{4}}{( x + 1 ) ^{9}})

- 8.314 \cdot ln (\frac{1}{10})

\frac{1}{2} ln (\frac{2}{3})

ln (18) - ln (8)

lo g_{7} (19 w)

What is ln(27)+ln(9)-ln(1/3)*4ln(sqrt(3)) ?
The solution to ln(27)+ln(9)-ln(1/3)*4ln(sqrt(3)) is 5ln(3)+2ln^2(3)