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

The solution to ln(6)-ln(7)-ln(2)+ln(3) is ln(9/7)

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

simplify

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

ln (\frac{9}{7})

Decimal Notation

0.25131 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{\frac{6}{7}}{2} = \frac{3}{7}

= ln (\frac{3}{7}) + ln (3)

Apply log rule:

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

ln (\frac{3}{7}) + ln (3) = ln (3 \cdot \frac{3}{7})

= ln (3 \cdot \frac{3}{7})

\frac{3}{7} \cdot 3 = \frac{9}{7}

= ln (\frac{9}{7})

- lo g_{10} (1.89 \cdot 1 0^{- 3})

ln (\frac{30}{42})

0.25 ln (2) + 1.75 ln (3) + 5.5 ln (2)

24 (136 ln^{2} (7) - 4 ln^{2} (5))

6.1 + lo g_{10} (\frac{24}{( 0.03 \cdot 30 )})

What is ln(6)-ln(7)-ln(2)+ln(3) ?
The solution to ln(6)-ln(7)-ln(2)+ln(3) is ln(9/7)