What is 7/6+2ln(2)-ln(3)-5(ln(6)-ln(5)) ?

The solution to 7/6+2ln(2)-ln(3)-5(ln(6)-ln(5)) is 7/6+ln(3125/5832)

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simplify 7/6+2ln(2)-ln(3)-5(ln(6)-ln(5))

simplify

\frac{7}{6} + 2 ln (2) - ln (3) - 5 (ln (6) - ln (5))

\frac{7}{6} + ln (\frac{3125}{5832})

Decimal Notation

0.54274 \dots

Solution steps

\frac{7}{6} + 2 ln (2) - ln (3) - 5 (ln (6) - ln (5))

Apply log rule:

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

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

= \frac{7}{6} + ln (2^{2}) - ln (3) - 5 (ln (6) - ln (5))

Apply log rule:

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

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

= \frac{7}{6} + ln (\frac{2 ^{2}}{3}) - 5 (ln (6) - ln (5))

2^{2} = 4

= \frac{7}{6} + ln (\frac{4}{3}) - 5 (ln (6) - ln (5))

Apply log rule:

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

ln (6) - ln (5) = ln (\frac{6}{5})

= \frac{7}{6} + ln (\frac{4}{3}) - 5 ln (\frac{6}{5})

Apply log rule:

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

5 ln (\frac{6}{5}) = ln ((\frac{6}{5})^{5})

= \frac{7}{6} + ln (\frac{4}{3}) - ln ((\frac{6}{5})^{5})

Apply log rule:

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

ln (\frac{4}{3}) - ln ((\frac{6}{5})^{5}) = ln (\frac{\frac{4}{3}}{( \frac{6}{5} ) ^{5}})

= \frac{7}{6} + ln (\frac{\frac{4}{3}}{( \frac{6}{5} ) ^{5}})

\frac{\frac{4}{3}}{( \frac{6}{5} ) ^{5}} = \frac{3125}{5832}

= \frac{7}{6} + ln (\frac{3125}{5832})

ln (a b^{x})

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

lo g_{10} (x^{3} z)

2 ln (x) + 3 ln (y) - 4 ln (z)

\frac{9 ln ( 5 )}{2 ln ( 3 ) - ln ( 5 )}

What is 7/6+2ln(2)-ln(3)-5(ln(6)-ln(5)) ?
The solution to 7/6+2ln(2)-ln(3)-5(ln(6)-ln(5)) is 7/6+ln(3125/5832)