What is ln((86-65)/(86-50)) ?

The solution to ln((86-65)/(86-50)) is ln(21)-2ln(6)

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simplify ln((86-65)/(86-50))

simplify

ln (\frac{86 - 65}{86 - 50})

ln (21) - 2 ln (6)

Decimal Notation

- 0.53899 \dots

Solution steps

ln (\frac{86 - 65}{86 - 50})

Apply log rule:

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

ln (\frac{86 - 65}{86 - 50}) = ln (86 - 65) - ln (86 - 50)

= ln (86 - 65) - ln (86 - 50)

Subtract the numbers:

86 - 65 = 21

= ln (21) - ln (86 - 50)

Subtract the numbers:

86 - 50 = 36

= ln (21) - ln (36)

ln (36) = 2 ln (6)

= ln (21) - 2 ln (6)

lo g_{b} (x) + 2 lo g_{b} (y)

ln (\frac{4}{27})

ln (\frac{3}{2}) - 1

ln (10) - 3 ln (6)

2 ln (3 x) + ln (x - 1)

What is ln((86-65)/(86-50)) ?
The solution to ln((86-65)/(86-50)) is ln(21)-2ln(6)