What is ln((2sqrt(3))/3)-ln(1) ?

The solution to ln((2sqrt(3))/3)-ln(1) is ln(2)-1/2 ln(3)

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simplify ln((2sqrt(3))/3)-ln(1)

simplify

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

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

Decimal Notation

0.14384 \dots

Solution steps

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

Apply log rule:

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

ln (\frac{2 3}{3}) = ln (23) - ln (3)

= ln (23) - ln (3) - ln (1)

Apply log rule:

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

ln (23) = ln (2) + ln (3)

= ln (2) + ln (3) - ln (3) - ln (1)

ln (3) = \frac{1}{2} ln (3)

ln (1) = 0

= ln (2) + \frac{1}{2} ln (3) - ln (3) - 0

Add similar elements:

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

= ln (2) - \frac{1}{2} ln (3) - 0

ln (2) - \frac{1}{2} ln (3) - 0 = ln (2) - \frac{1}{2} ln (3)

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

\frac{1}{2} [ln (x) + 2 ln (x + 1)] + 3 ln (x - 5)

ln (3 x^{4} (y^{2} - 3)^{3})

\frac{4}{3 ln ( 3 )} + \frac{10}{3} - \frac{2}{ln ( 2 )}

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

ln (3) - ln (3 - x)

What is ln((2sqrt(3))/3)-ln(1) ?
The solution to ln((2sqrt(3))/3)-ln(1) is ln(2)-1/2 ln(3)