What is 2ln(sqrt(2))+3ln(sqrt(3)) ?

The solution to 2ln(sqrt(2))+3ln(sqrt(3)) is ln(6sqrt(3))

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simplify 2ln(sqrt(2))+3ln(sqrt(3))

simplify

2 ln (2) + 3 ln (3)

ln (63)

Decimal Notation

2.34106 \dots

Solution steps

2 ln (2) + 3 ln (3)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

(2)^{2} (3)^{3} = 63

= ln (63)

ln (\frac{0.063}{0.0295})

lo g_{8} (2 - x) + lo g_{8} (4 - x)

0.2 ln (30) + 0.8 ln (5)

- \frac{( 1 )}{( 2 )} ln^{4} (x^{2}) - \frac{( 1 )}{( 2 )} ln (x^{2})

What is 2ln(sqrt(2))+3ln(sqrt(3)) ?
The solution to 2ln(sqrt(2))+3ln(sqrt(3)) is ln(6sqrt(3))