What is ln(sqrt(3))*ln(sqrt(3)) ?

The solution to ln(sqrt(3))*ln(sqrt(3)) is 1/4 ln^2(3)

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simplify ln(sqrt(3))*ln(sqrt(3))

simplify

ln (3) \cdot ln (3)

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

Decimal Notation

0.30173 \dots

Solution steps

ln (3) ln (3)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

ln (3) ln (3) = ln^{1 + 1} (3)

= ln^{1 + 1} (3)

Add the numbers:

1 + 1 = 2

= ln^{2} (3)

Simplify

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

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

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

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

Apply rule

1^{a} = 1

1^{2} = 1

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

2^{2} = 4

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

4 π \cdot 1 0^{- 7} \cdot 80 \cdot 3

e^{- n l n (1 - β x)}

2^{c s c (4 x)}

What is ln(sqrt(3))*ln(sqrt(3)) ?
The solution to ln(sqrt(3))*ln(sqrt(3)) is 1/4 ln^2(3)