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

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

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

simplify

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

- 4 ln (2)

Decimal Notation

- 2.77258 \dots

Solution steps

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

Apply log rule:

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

ln (\frac{1}{4}) = ln (1) - ln (4)

= - ln (4) + + ln (1) - ln (4)

Simplify

- ln (4) + + ln (1) - ln (4) : - 2 ln (4) + ln (1)

Apply log rule:

lo g_{a} (1) = 0

= - 2 ln (4) + 0

- 2 ln (4) + 0 = - 2 ln (4)

= - 2 ln (4)

Simplify

ln (4) : 2 ln (2)

= - 2 \cdot 2 ln (2)

Multiply the numbers:

2 \cdot 2 = 4

= - 4 ln (2)

ln (20) - ln (9)

lo g_{2} (x^{6} y^{4})

3 lo g_{5} (x + 2) - lo g_{5} (x)

ln (6 + x) - ln (x)

- lo g_{10} (9.2 \cdot 1 0^{- 6})

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