What is 4ln(4)-6ln(3)+2ln(2)-2 ?

The solution to 4ln(4)-6ln(3)+2ln(2)-2 is ln(1024/729)-2

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simplify 4ln(4)-6ln(3)+2ln(2)-2

simplify

4 ln (4) - 6 ln (3) + 2 ln (2) - 2

ln (\frac{1024}{729}) - 2

Decimal Notation

- 1.66020 \dots

Solution steps

4 ln (4) - 6 ln (3) + 2 ln (2) - 2

Apply log rule:

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

4 ln (4) = ln (4^{4})

= ln (4^{4}) - 6 ln (3) + 2 ln (2) - 2

Apply log rule:

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

6 ln (3) = ln (3^{6})

= ln (4^{4}) - ln (3^{6}) + 2 ln (2) - 2

Apply log rule:

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

ln (4^{4}) - ln (3^{6}) = ln (\frac{4 ^{4}}{3 ^{6}})

= ln (\frac{4 ^{4}}{3 ^{6}}) + 2 ln (2) - 2

\frac{4 ^{4}}{3 ^{6}} = \frac{256}{729}

= ln (\frac{256}{729}) + 2 ln (2) - 2

Apply log rule:

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

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

= ln (\frac{256}{729}) + ln (2^{2}) - 2

Apply log rule:

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

ln (\frac{256}{729}) + ln (2^{2}) = ln (2^{2} \cdot \frac{256}{729})

= ln (2^{2} \cdot \frac{256}{729}) - 2

\frac{256}{729} \cdot 2^{2} = \frac{1024}{729}

= ln (\frac{1024}{729}) - 2

2 ln (e^{a}) + 3 ln (b^{e})

lo g_{10} (z^{8} y)

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

ln (10) + 2 ln (x) + 3 ln (x^{2} + 10)

2 ln (2) + ln (\frac{5}{3})

What is 4ln(4)-6ln(3)+2ln(2)-2 ?
The solution to 4ln(4)-6ln(3)+2ln(2)-2 is ln(1024/729)-2