What is ln(65000)-ln(61000) ?

The solution to ln(65000)-ln(61000) is ln(65/61)

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simplify ln(65000)-ln(61000)

simplify

ln (65000) - ln (61000)

ln (\frac{65}{61})

Decimal Notation

0.06351 \dots

Solution steps

ln (65000) - ln (61000)

Apply log rule:

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

ln (65000) - ln (61000) = ln (\frac{65000}{61000})

= ln (\frac{65000}{61000})

Cancel the common factor:

1000

= ln (\frac{65}{61})

ln (336 \cdot 1 0^{4})

\frac{ln ( 4 )}{ln ( 4 ) - 2 ln ( 3 )}

3 lo g_{5} (a) + 4 lo g_{5} (b)

2 ln (4) + 2 ln (3)

ln (\frac{4 x - 3}{x})