What is simplify-1/2 ln(4)+ln(3)+3/2 ln(2)-3/2 ln(1) ?

The solution to simplify-1/2 ln(4)+ln(3)+3/2 ln(2)-3/2 ln(1) is ln(3sqrt(2))

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simplify-1/2 ln(4)+ln(3)+3/2 ln(2)-3/2 ln(1)

simplify

- \frac{1}{2} ln (4) + ln (3) + \frac{3}{2} ln (2) - \frac{3}{2} ln (1)

ln (32)

Decimal Notation

1.44518 \dots

Solution steps

- \frac{1}{2} ln (4) + ln (3) + \frac{3}{2} ln (2) - \frac{3}{2} ln (1)

Apply log rule:

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

\frac{1}{2} ln (4) = ln (4^{\frac{1}{2}})

= - ln (4^{\frac{1}{2}}) + ln (3) + \frac{3}{2} ln (2) - \frac{3}{2} ln (1)

Apply log rule:

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

ln (3) - ln (4^{\frac{1}{2}}) = ln (\frac{3}{4 ^{\frac{1}{2}}})

= ln (\frac{3}{4 ^{\frac{1}{2}}}) + \frac{3}{2} ln (2) - \frac{3}{2} ln (1)

4^{\frac{1}{2}} = 2

= ln (\frac{3}{2}) + \frac{3}{2} ln (2) - \frac{3}{2} ln (1)

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}}) - \frac{3}{2} ln (1)

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} ln (1)

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

= ln (32) - \frac{3}{2} ln (1)

\frac{3}{2} ln (1) = 0

= ln (32) - 0

ln (32) - 0 = ln (32)

= ln (32)

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

e^{2 l n ∣ l n (x) ∣ + l n (x)}

lo g_{10} (1.2 e^{- 3})

ln (A e^{\frac{3}{2} t^{2}})

ln ∣ 4 ∣ + 2 ln (4^{2} + 4) - ln ∣ 1 ∣ + 2 ln (1^{2} + 4)

What is simplify-1/2 ln(4)+ln(3)+3/2 ln(2)-3/2 ln(1) ?
The solution to simplify-1/2 ln(4)+ln(3)+3/2 ln(2)-3/2 ln(1) is ln(3sqrt(2))