What is (ln(11000)-ln(7000))/3 ?

The solution to (ln(11000)-ln(7000))/3 is (ln(11/7))/3

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simplify (ln(11000)-ln(7000))/3

simplify

\frac{ln ( 11000 ) - ln ( 7000 )}{3}

\frac{ln ( \frac{11}{7} )}{3}

Decimal Notation

0.15066 \dots

Solution steps

\frac{ln ( 11000 ) - ln ( 7000 )}{3}

Apply log rule:

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

ln (11000) - ln (7000) = ln (\frac{11000}{7000})

= \frac{ln ( \frac{11000}{7000} )}{3}

Cancel the common factor:

1000

= \frac{ln ( \frac{11}{7} )}{3}

ln (\frac{58387}{88}) \cdot (- \frac{80}{3})

ln (x) + \frac{1}{2} ln (\frac{x ^{2} + y ^{2}}{x ^{2}})

3 ln (4) + 3 ln (3)

ln (\frac{2}{x ^{2} + 6})

ln (\frac{1}{2} x^{0.5} \cdot y^{0.5})

What is (ln(11000)-ln(7000))/3 ?
The solution to (ln(11000)-ln(7000))/3 is (ln(11/7))/3