What is simplify-2ln(3)-2ln(2)+2ln(7) ?

The solution to simplify-2ln(3)-2ln(2)+2ln(7) is ln(49/36)

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simplify-2ln(3)-2ln(2)+2ln(7)

simplify

- 2 ln (3) - 2 ln (2) + 2 ln (7)

ln (\frac{49}{36})

Decimal Notation

0.30830 \dots

Solution steps

- 2 ln (3) - 2 ln (2) + 2 ln (7)

Apply log rule:

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

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

= - ln (3^{2}) - 2 ln (2) + 2 ln (7)

Apply log rule:

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

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

= - ln (3^{2}) - ln (2^{2}) + 2 ln (7)

Rewrite

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

- (ln (3^{2}) + ln (2^{2}))

= - (ln (3^{2}) + ln (2^{2})) + 2 ln (7)

Apply log rule:

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

ln (3^{2}) + ln (2^{2}) = ln (3^{2} \cdot 2^{2})

= - ln (3^{2} \cdot 2^{2}) + 2 ln (7)

3^{2} \cdot 2^{2} = 36

= - ln (36) + 2 ln (7)

Apply log rule:

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

2 ln (7) = ln (7^{2})

= - ln (36) + ln (7^{2})

Apply log rule:

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

ln (7^{2}) - ln (36) = ln (\frac{7 ^{2}}{36})

= ln (\frac{7 ^{2}}{36})

7^{2} = 49

= ln (\frac{49}{36})

ln (\frac{31.53}{31.53 - ( 0.01 \cdot 1400 )})

ln (x) + ln (x - 1) 2

- 3 ln (13) + 3 ln (18)

ln (92) - ln (x)

- 0.67 lo g_{2} (0.67) - 0.33 lo g_{2} (0.33)

What is simplify-2ln(3)-2ln(2)+2ln(7) ?
The solution to simplify-2ln(3)-2ln(2)+2ln(7) is ln(49/36)