What is ln(6)+ln(3)-ln(8)-ln(5) ?

The solution to ln(6)+ln(3)-ln(8)-ln(5) is ln(9/20)

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simplify ln(6)+ln(3)-ln(8)-ln(5)

simplify

ln (6) + ln (3) - ln (8) - ln (5)

ln (\frac{9}{20})

Decimal Notation

- 0.79850 \dots

Solution steps

ln (6) + ln (3) - ln (8) - ln (5)

Apply log rule:

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

ln (6) + ln (3) = ln (6 \cdot 3)

= ln (6 \cdot 3) - ln (8) - ln (5)

Multiply the numbers:

6 \cdot 3 = 18

= ln (18) - ln (8) - ln (5)

Apply log rule:

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

ln (18) - ln (8) = ln (\frac{18}{8})

= ln (\frac{18}{8}) - ln (5)

Cancel the common factor:

2

= ln (\frac{9}{4}) - ln (5)

Apply log rule:

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

ln (\frac{9}{4}) - ln (5) = ln (\frac{\frac{9}{4}}{5})

= ln (\frac{\frac{9}{4}}{5})

\frac{\frac{9}{4}}{5} = \frac{9}{20}

= ln (\frac{9}{20})

- ln (2.54 e^{- 5})

ln (x - 3) - ln (x - 7) + 10 ln (x)

ln (4 \cdot 2)

ln (\frac{1000000}{465663})

- ln (\frac{5}{a ^{- 2}})

What is ln(6)+ln(3)-ln(8)-ln(5) ?
The solution to ln(6)+ln(3)-ln(8)-ln(5) is ln(9/20)