What is simplify-ln(4/3) ?

The solution to simplify-ln(4/3) is -2ln(2)+ln(3)

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simplify-ln(4/3)

simplify

- ln (\frac{4}{3})

- 2 ln (2) + ln (3)

Decimal Notation

- 0.28768 \dots

Solution steps

- ln (\frac{4}{3})

Apply log rule:

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

ln (\frac{4}{3}) = ln (4) - ln (3)

= - (ln (4) - ln (3))

ln (4) = 2 ln (2)

= - (2 ln (2) - ln (3))

Distribute parentheses

= - (2 ln (2)) - (- ln (3))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 2 ln (2) + ln (3)

\frac{1}{2} ln (\frac{3}{4}) - \frac{1}{2} ln (\frac{1}{2})

\frac{1}{3} lo g_{2} (3)

5 lo g_{5} (7 y + 1) + \frac{1}{2} lo g_{5} (y + 5)

ln (\frac{2 x}{a ^{2}})

6 lo g_{5} (z - 4) - 3 lo g_{5} (z + 5)