What is ln((1/3)/(1/59049)) ?

The solution to ln((1/3)/(1/59049)) is 9ln(3)

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simplify ln((1/3)/(1/59049))

simplify

ln (\frac{\frac{1}{3}}{\frac{1}{59049}})

9 ln (3)

Decimal Notation

9.88751 \dots

Solution steps

ln (\frac{\frac{1}{3}}{\frac{1}{59049}})

Apply log rule:

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

ln (\frac{\frac{1}{3}}{\frac{1}{59049}}) = ln (\frac{1}{3}) - ln (\frac{1}{59049})

= ln (\frac{1}{3}) - ln (\frac{1}{59049})

Apply log rule:

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

ln (\frac{1}{3}) = ln (1) - ln (3), ln (\frac{1}{59049}) = ln (1) - ln (59049)

= ln (1) - ln (3) - (ln (1) - ln (59049))

ln (1) = 0

- (ln (1) - ln (59049)) = 10 ln (3)

= 0 - ln (3) + 10 ln (3)

Add similar elements:

- ln (3) + 10 ln (3) = 9 ln (3)

= 0 + 9 ln (3)

0 + 9 ln (3) = 9 ln (3)

= 9 ln (3)

ln (\frac{11}{10})

ln (25) + ln (2)

7 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

lo g_{10} (2) - \frac{1}{2 ln ( 10 )}

6 ln (6) - 4 ln (4) - 2