What is [2ln(3)-2ln(9)]-[2ln(2)-2ln(7)] ?

The solution to [2ln(3)-2ln(9)]-[2ln(2)-2ln(7)] is -2ln(3)-ln(4/49)

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simplify [2ln(3)-2ln(9)]-[2ln(2)-2ln(7)]

simplify

[2 ln (3) - 2 ln (9)] - [2 ln (2) - 2 ln (7)]

- 2 ln (3) - ln (\frac{4}{49})

Decimal Notation

0.30830 \dots

Solution steps

[2 ln (3) - 2 ln (9)] - [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})

= [2 ln (3) - 2 ln (9)] - [ln (2^{2}) - 2 ln (7)]

Apply log rule:

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

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

= [2 ln (3) - 2 ln (9)] - [ln (2^{2}) - ln (7^{2})]

Apply log rule:

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

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

= [2 ln (3) - 2 ln (9)] - [ln (\frac{2 ^{2}}{7 ^{2}})]

\frac{2 ^{2}}{7 ^{2}} = \frac{4}{49}

= [2 ln (3) - 2 ln (9)] - [ln (\frac{4}{49})]

Remove parentheses:

(a) = a

= 2 ln (3) - 2 ln (9) - ln (\frac{4}{49})

2 ln (9) = 4 ln (3)

= 2 ln (3) - 4 ln (3) - ln (\frac{4}{49})

Add similar elements:

2 ln (3) - 4 ln (3) = - 2 ln (3)

= - 2 ln (3) - ln (\frac{4}{49})

5 lo g_{10} (x) - 15 lo g_{10} (y)

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

lo g_{10} (x^{3}) y lo g_{10} (x) 3 y

lo g_{3} ((\frac{n ^{3}}{m})^{6})

12 ln (2 x) - tan (4 x)

What is [2ln(3)-2ln(9)]-[2ln(2)-2ln(7)] ?
The solution to [2ln(3)-2ln(9)]-[2ln(2)-2ln(7)] is -2ln(3)-ln(4/49)