What is ln(2)+2*ln(6)-ln(6) ?

The solution to ln(2)+2*ln(6)-ln(6) is ln(12)

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simplify ln(2)+2*ln(6)-ln(6)

simplify

ln (2) + 2 \cdot ln (6) - ln (6)

ln (12)

Decimal Notation

2.48490 \dots

Solution steps

ln (2) + 2 ln (6) - ln (6)

Apply log rule:

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

2 ln (6) = ln (6^{2})

= ln (2) + ln (6^{2}) - ln (6)

Apply log rule:

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

ln (2) + ln (6^{2}) = ln (6^{2} \cdot 2)

= ln (6^{2} \cdot 2) - ln (6)

2 \cdot 6^{2} = 72

= ln (72) - ln (6)

Apply log rule:

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

ln (72) - ln (6) = ln (\frac{72}{6})

= ln (\frac{72}{6})

Divide the numbers:

\frac{72}{6} = 12

= ln (12)

\frac{ln ( n ) - 2 ln ( Θ )}{2 ln ( n )}

lo g_{e} (\frac{2 x - 1}{x - 1})

lo g_{e} (0.4 p) - lo g_{e} (p)

3 [2 ln (x - 1) - ln (x)] + ln (x + 1)

\frac{1}{8} ln (2)