What is simplify-ln(75)-3ln(15/22) ?

The solution to simplify-ln(75)-3ln(15/22) is -ln(253125/10648)

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simplify-ln(75)-3ln(15/22)

simplify

- ln (75) - 3 ln (\frac{15}{22})

- ln (\frac{253125}{10648})

Decimal Notation

- 3.16851 \dots

Solution steps

- ln (75) - 3 ln (\frac{15}{22})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (\frac{15}{22}) = ln ((\frac{15}{22})^{3})

= - ln (75) - ln ((\frac{15}{22})^{3})

Rewrite

- ln (75) - ln ((\frac{15}{22})^{3})

- (ln (75) + ln ((\frac{15}{22})^{3}))

= - (ln (75) + ln ((\frac{15}{22})^{3}))

Apply log rule:

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

ln (75) + ln ((\frac{15}{22})^{3}) = ln (75 (\frac{15}{22})^{3})

= - ln (75 (\frac{15}{22})^{3})

75 (\frac{15}{22})^{3} = \frac{253125}{10648}

= - ln (\frac{253125}{10648})

ln (0.3 e^{4})

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

ln (\frac{\frac{1}{2}}{0.144})

\frac{25 ln ( 3 ) - 9 ln ( 5 )}{8} + 1

\frac{1}{144} ln (2)

What is simplify-ln(75)-3ln(15/22) ?
The solution to simplify-ln(75)-3ln(15/22) is -ln(253125/10648)