What is 3.3ln(6)-7.2ln(2)-0.9ln(2) ?

The solution to 3.3ln(6)-7.2ln(2)-0.9ln(2) is ln(1.34758…)

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simplify 3.3ln(6)-7.2ln(2)-0.9ln(2)

simplify

3.3 ln (6) - 7.2 ln (2) - 0.9 ln (2)

ln (1.34758 \dots)

Decimal Notation

0.29831 \dots

Solution steps

3.3 ln (6) - 7.2 ln (2) - 0.9 ln (2)

Apply log rule:

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

3.3 ln (6) = ln (6^{3.3})

= ln (6^{3.3}) - 7.2 ln (2) - 0.9 ln (2)

Apply log rule:

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

7.2 ln (2) = ln (2^{7.2})

= ln (6^{3.3}) - ln (2^{7.2}) - 0.9 ln (2)

Apply log rule:

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

ln (6^{3.3}) - ln (2^{7.2}) = ln (\frac{6 ^{3.3}}{2 ^{7.2}})

= ln (\frac{6 ^{3.3}}{2 ^{7.2}}) - 0.9 ln (2)

\frac{6 ^{3.3}}{2 ^{7.2}} = 2.51468 \dots

= ln (2.51468 \dots) - 0.9 ln (2)

Apply log rule:

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

0.9 ln (2) = ln (2^{0.9})

= ln (2.51468 \dots) - ln (2^{0.9})

Apply log rule:

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

ln (2.51468 \dots) - ln (2^{0.9}) = ln (\frac{2.51468 \dots}{2 ^{0.9}})

= ln (\frac{2.51468 \dots}{2 ^{0.9}})

\frac{2.51468 \dots}{2 ^{0.9}} = 1.34758 \dots

= ln (1.34758 \dots)

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- ln (x y)

What is 3.3ln(6)-7.2ln(2)-0.9ln(2) ?
The solution to 3.3ln(6)-7.2ln(2)-0.9ln(2) is ln(1.34758…)