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Popular >

simplify ln((22)/(32))

Solution

simplify

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

Solution

ln (2) - ln (3)

+1

Solution steps

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

Apply log rule:

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

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

= ln (2 \cdot 2) - ln (3 \cdot 2)

Apply log rule:

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

ln (2 \cdot 2) = ln (2) + ln (2), ln (3 \cdot 2) = ln (3) + ln (2)

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

Add similar elements:

ln (2) + ln (2) = 2 ln (2)

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

- (ln (3) + ln (2)) : - ln (3) - ln (2)

= 2 ln (2) - ln (3) - ln (2)

Simplify

2 ln (2) - ln (3) - ln (2) : ln (2) - ln (3)

= ln (2) - ln (3)

Popular Examples

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

simplify-192ln((0.0001)/(0.04))simplify

- 192 ln (\frac{0.0001}{0.04})

simplify-log_{10}(1.33*10^{-12})simplify

- lo g_{10} (1.33 \cdot 1 0^{- 12})

simplify 5ln(x+1)+2ln(x^3)-ln(x)simplify

5 ln (x + 1) + 2 ln (x^{3}) - ln (x)

simplify 0.5log_{10}(c)+5log_{10}(d)simplify

0.5 lo g_{10} (c) + 5 lo g_{10} (d)

Frequently Asked Questions (FAQ)

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