What is 2ln(5)+7/5-2ln(-3)-7/3 ?

The solution to 2ln(5)+7/5-2ln(-3)-7/3 is ln(25/9)-14/15

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simplify 2ln(5)+7/5-2ln(-3)-7/3

simplify

2 ln (5) + \frac{7}{5} - 2 ln (- 3) - \frac{7}{3}

ln (\frac{25}{9}) - \frac{14}{15}

Decimal Notation

0.08831 \dots

Solution steps

2 ln (5) + \frac{7}{5} - 2 ln (- 3) - \frac{7}{3}

Apply log rule:

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

2 ln (5) = ln (5^{2})

= ln (5^{2}) + \frac{7}{5} - 2 ln (- 3) - \frac{7}{3}

Apply log rule:

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

2 ln (- 3) = ln ((- 3)^{2})

= ln (5^{2}) + \frac{7}{5} - ln ((- 3)^{2}) - \frac{7}{3}

Apply log rule:

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

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

= ln (\frac{5 ^{2}}{( - 3 ) ^{2}}) + \frac{7}{5} - \frac{7}{3}

\frac{5 ^{2}}{( - 3 ) ^{2}} = \frac{25}{9}

= ln (\frac{25}{9}) + \frac{7}{5} - \frac{7}{3}

Combine the fractions

\frac{7}{5} - \frac{7}{3} : - \frac{14}{15}

= ln (\frac{25}{9}) - \frac{14}{15}

5 lo g_{10} (a x) + 3 lo g_{10} (a) y

\frac{19}{2} lo g_{2} (\frac{7}{5}) - \frac{19}{2}

lo g_{r} (11 x)

ln (x) + ln (y) + ln (z)

What is 2ln(5)+7/5-2ln(-3)-7/3 ?
The solution to 2ln(5)+7/5-2ln(-3)-7/3 is ln(25/9)-14/15