What is (25(ln(-3)-ln(-15)))/(ln(2/3)) ?

The solution to (25(ln(-3)-ln(-15)))/(ln(2/3)) is -(25ln(5))/(ln(2/3))

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simplify (25(ln(-3)-ln(-15)))/(ln(2/3))

simplify

\frac{25 ( ln ( - 3 ) - ln ( - 15 ) )}{ln ( \frac{2}{3} )}

- \frac{25 ln ( 5 )}{ln ( \frac{2}{3} )}

Decimal Notation

99.23405 \dots

Solution steps

\frac{25 ( ln ( - 3 ) - ln ( - 15 ) )}{ln ( \frac{2}{3} )}

Apply log rule:

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

ln (- 3) - ln (- 15) = ln (\frac{- 3}{- 15})

= \frac{25 ln ( \frac{- 3}{- 15} )}{ln ( \frac{2}{3} )}

\frac{- 3}{- 15} = \frac{1}{5}

= \frac{25 ln ( \frac{1}{5} )}{ln ( \frac{2}{3} )}

Simplify

ln (\frac{1}{5}) : - ln (5)

= \frac{25 ( - ln ( 5 ) )}{ln ( \frac{2}{3} )}

Remove parentheses:

(- a) = - a

= \frac{- 25 ln ( 5 )}{ln ( \frac{2}{3} )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{25 ln ( 5 )}{ln ( \frac{2}{3} )}

ln (x^{2} - 1) - ln (x - 1)

5 ln (u) - 2 ln (6)

lo g_{4} (5) + lo g_{4} (16) + lo g_{4} (1.25)

ln (\frac{25.65}{95})

lo g_{5} (3 x^{2}) + ln (4 x^{3})

What is (25(ln(-3)-ln(-15)))/(ln(2/3)) ?
The solution to (25(ln(-3)-ln(-15)))/(ln(2/3)) is -(25ln(5))/(ln(2/3))