simplify ln(8*12)

Solution

simplify

ln (8 \cdot 12)

3 ln (2) + ln (12)

Decimal Notation

4.56434 \dots

Solution steps

ln (8 \cdot 12)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (8 \cdot 12) = ln (8) + ln (12)

= ln (8) + ln (12)

ln (8) = 3 ln (2)

= 3 ln (2) + ln (12)

ln (\frac{( 75 + x )}{75})

\frac{1}{ln ( 2 )} \cdot ln (\frac{4}{3})

(0.287) ln (\frac{500}{200}) - (1.05) ln (\frac{680}{980})

lo g_{e} (25) + lo g_{e} (4)

\frac{8}{5} ln (\frac{4}{3}) + \frac{9}{10} ln (\frac{81}{77})