What is ln(104)-2ln(104/77) ?

The solution to ln(104)-2ln(104/77) is ln(5929/104)

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simplify ln(104)-2ln(104/77)

simplify

ln (104) - 2 ln (\frac{104}{77})

ln (\frac{5929}{104})

Decimal Notation

4.04321 \dots

Solution steps

ln (104) - 2 ln (\frac{104}{77})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (\frac{104}{77}) = ln ((\frac{104}{77})^{2})

= ln (104) - ln ((\frac{104}{77})^{2})

Apply log rule:

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

ln (104) - ln ((\frac{104}{77})^{2}) = ln (\frac{104}{( \frac{104}{77} ) ^{2}})

= ln (\frac{104}{( \frac{104}{77} ) ^{2}})

\frac{104}{( \frac{104}{77} ) ^{2}} = \frac{5929}{104}

= ln (\frac{5929}{104})

7 lo g_{2} (x) - 4 lo g_{2} (y)

ln (\frac{a x}{56})

6.1 + lo g_{10} (\frac{24}{1.2})

lo g_{10} (a) - 3 lo g_{10} (b) - 3

lo g_{10} (2) + 2 lo g_{10} (x)

What is ln(104)-2ln(104/77) ?
The solution to ln(104)-2ln(104/77) is ln(5929/104)