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

The solution to simplify-ln(2)+ln(3)+3/2 ln(2) is ln(3sqrt(2))

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

simplify

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

ln (32)

Decimal Notation

1.44518 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{3}{2} \cdot 2^{\frac{3}{2}} = 32

= ln (32)

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What is simplify-ln(2)+ln(3)+3/2 ln(2) ?
The solution to simplify-ln(2)+ln(3)+3/2 ln(2) is ln(3sqrt(2))