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Popular >

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

Solution

simplify

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

Solution

2 ln (3)

+1

Decimal Notation

2.19722 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{1 + 2}{1 - \frac{2}{3}} = 9

= ln (9)

Rewrite

9

in power-base form:

9 = 3^{2}

= ln (3^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (3^{2}) = 2 ln (3)

= 2 ln (3)

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Frequently Asked Questions (FAQ)

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