What is simplify-ln(7.8-3)+2ln(7.8-2)+C ?

The solution to simplify-ln(7.8-3)+2ln(7.8-2)+C is ln(7.00833…)+C

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simplify-ln(7.8-3)+2ln(7.8-2)+C

simplify

- ln (7.8 - 3) + 2 ln (7.8 - 2) + C

ln (7.00833 \dots) + C

Solution steps

- ln (7.8 - 3) + 2 ln (7.8 - 2) + C

Apply log rule:

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

2 ln (7.8 - 2) = ln ((7.8 - 2)^{2})

= - ln (7.8 - 3) + ln ((7.8 - 2)^{2}) + C

Apply log rule:

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

ln ((7.8 - 2)^{2}) - ln (7.8 - 3) = ln (\frac{( 7.8 - 2 ) ^{2}}{7.8 - 3})

= ln (\frac{( 7.8 - 2 ) ^{2}}{7.8 - 3}) + C

\frac{( 7.8 - 2 ) ^{2}}{7.8 - 3} = 7.00833 \dots

= ln (7.00833 \dots) + C

2 lo g_{3} (x) - \frac{1}{2} lo g_{3} (y) + lo g_{3} (z)

8 lo g_{6} (x) + 2 lo g_{6} (z)

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

ln (3 x) + ln (2 y)

\frac{1}{3} \cdot ln (\frac{3 + 5}{2})

What is simplify-ln(7.8-3)+2ln(7.8-2)+C ?
The solution to simplify-ln(7.8-3)+2ln(7.8-2)+C is ln(7.00833…)+C