What is 4(ln(3)-ln(2))+6(ln(7)-ln(6)) ?

The solution to 4(ln(3)-ln(2))+6(ln(7)-ln(6)) is ln(117649/9216)

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simplify 4(ln(3)-ln(2))+6(ln(7)-ln(6))

simplify

4 (ln (3) - ln (2)) + 6 (ln (7) - ln (6))

ln (\frac{117649}{9216})

Decimal Notation

2.54676 \dots

Solution steps

4 (ln (3) - ln (2)) + 6 (ln (7) - ln (6))

Apply log rule:

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

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

= 4 ln (\frac{3}{2}) + 6 (ln (7) - ln (6))

Apply log rule:

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

ln (7) - ln (6) = ln (\frac{7}{6})

= 4 ln (\frac{3}{2}) + 6 ln (\frac{7}{6})

Apply log rule:

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

4 ln (\frac{3}{2}) = ln ((\frac{3}{2})^{4})

= ln ((\frac{3}{2})^{4}) + 6 ln (\frac{7}{6})

Apply log rule:

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

6 ln (\frac{7}{6}) = ln ((\frac{7}{6})^{6})

= ln ((\frac{3}{2})^{4}) + ln ((\frac{7}{6})^{6})

Apply log rule:

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

ln ((\frac{3}{2})^{4}) + ln ((\frac{7}{6})^{6}) = ln ((\frac{7}{6})^{6} (\frac{3}{2})^{4})

= ln ((\frac{7}{6})^{6} (\frac{3}{2})^{4})

(\frac{3}{2})^{4} (\frac{7}{6})^{6} = \frac{117649}{9216}

= ln (\frac{117649}{9216})

2 ln (\frac{α q}{α + 1})

lo g_{10} (\frac{x}{1000 y ^{3}})

\frac{1}{2} (- 5 lo g_{10} (x) + lo g_{10} (y z^{3}))

\frac{ln ( \frac{1034}{40353607} )}{2 ln ( 7 )}

lo g_{a} (5 x)

What is 4(ln(3)-ln(2))+6(ln(7)-ln(6)) ?
The solution to 4(ln(3)-ln(2))+6(ln(7)-ln(6)) is ln(117649/9216)