What is simplify-1/3 ln(1/3)-1/3 ln(1/3)-1/3 ln(1/3) ?

The solution to simplify-1/3 ln(1/3)-1/3 ln(1/3)-1/3 ln(1/3) is ln(3)

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simplify-1/3 ln(1/3)-1/3 ln(1/3)-1/3 ln(1/3)

simplify

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

ln (3)

Decimal Notation

1.09861 \dots

Solution steps

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

Apply log rule:

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

ln (\frac{1}{3}) = ln (1) - ln (3), ln (\frac{1}{3}) = ln (1) - ln (3), ln (\frac{1}{3}) = ln (1) - ln (3)

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

Add similar elements:

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

= - 1 \cdot (ln (1) - ln (3))

Apply log rule:

lo g_{a} (1) = 0

= - 1 \cdot (- ln (3) + 0)

0 - ln (3) = - ln (3)

= - 1 \cdot (- ln (3))

Apply rule

- (- a) = a

= 1 \cdot ln (3)

Multiply:

1 \cdot ln (3) = ln (3)

= ln (3)

ln (\frac{sin ( x )}{2})

- lo g_{10} (1.6 \cdot 1 0^{- 14})

- \frac{1}{2} ln ∣ 16 - 24 + 10 ∣ + \frac{1}{2} ln ∣ 10 ∣

ln (2) - ln (4) + ln (5)

35 e^{6} + ln (8) + 45 - ln (5)

What is simplify-1/3 ln(1/3)-1/3 ln(1/3)-1/3 ln(1/3) ?
The solution to simplify-1/3 ln(1/3)-1/3 ln(1/3)-1/3 ln(1/3) is ln(3)