What is simplify-ln(7/4) ?

The solution to simplify-ln(7/4) is -ln(7)+2ln(2)

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simplify-ln(7/4)

simplify

- ln (\frac{7}{4})

- ln (7) + 2 ln (2)

Decimal Notation

- 0.55961 \dots

Solution steps

- ln (\frac{7}{4})

Apply log rule:

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

ln (\frac{7}{4}) = ln (7) - ln (4)

= - (ln (7) - ln (4))

ln (4) = 2 ln (2)

= - (ln (7) - 2 ln (2))

Distribute parentheses

= - (ln (7)) - (- 2 ln (2))

Apply minus-plus rules

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

= - ln (7) + 2 ln (2)

- 5 (ln (x) + ln (y))

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

ln (\frac{0.42}{12})

25 lo g_{5} (3) + 50 lo g_{5} (x)

ln (\frac{1500000000}{824.26})