What is 9/10 ln(30)-12/5 ln(40) ?

The solution to 9/10 ln(30)-12/5 ln(40) is ln((2^{7/10}*3^{9/10}sqrt(5))/(3200))

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simplify 9/10 ln(30)-12/5 ln(40)

simplify

\frac{9}{10} ln (30) - \frac{12}{5} ln (40)

ln (\frac{2 ^{\frac{7}{10}} \cdot 3 ^{\frac{9}{10}} 5}{3200})

Decimal Notation

- 5.79223 \dots

Solution steps

\frac{9}{10} ln (30) - \frac{12}{5} ln (40)

Apply log rule:

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

\frac{9}{10} ln (30) = ln (3 0^{\frac{9}{10}})

= ln (3 0^{\frac{9}{10}}) - \frac{12}{5} ln (40)

Apply log rule:

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

\frac{12}{5} ln (40) = ln (4 0^{\frac{12}{5}})

= ln (3 0^{\frac{9}{10}}) - ln (4 0^{\frac{12}{5}})

Apply log rule:

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

ln (3 0^{\frac{9}{10}}) - ln (4 0^{\frac{12}{5}}) = ln (\frac{3 0 ^{\frac{9}{10}}}{4 0 ^{\frac{12}{5}}})

= ln (\frac{3 0 ^{\frac{9}{10}}}{4 0 ^{\frac{12}{5}}})

\frac{3 0 ^{\frac{9}{10}}}{4 0 ^{\frac{12}{5}}} = \frac{2 ^{\frac{7}{10}} \cdot 3 ^{\frac{9}{10}} 5}{3200}

= ln (\frac{2 ^{\frac{7}{10}} \cdot 3 ^{\frac{9}{10}} 5}{3200})

0.14 - \frac{0.0591}{2} \cdot lo g_{10} (\frac{1}{3})

ln ((1 + (10)^{2}) \cdot (- 20)^{2})

ln (x) - \frac{1}{4} ln (y)

- lo g_{10} (1.7 (1 0^{- 9}))

182000 (ln (0.44) - ln (1.3))

What is 9/10 ln(30)-12/5 ln(40) ?
The solution to 9/10 ln(30)-12/5 ln(40) is ln((2^{7/10}*3^{9/10}sqrt(5))/(3200))