What is ln(80)+ln(20) ?

The solution to ln(80)+ln(20) is 2ln(40)

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simplify ln(80)+ln(20)

simplify

ln (80) + ln (20)

2 ln (40)

Decimal

7.37775 \dots

Solution steps

ln (80) + ln (20)

Apply log rule:

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

ln (80) + ln (20) = ln (80 \cdot 20)

= ln (80 \cdot 20)

Multiply the numbers:

80 \cdot 20 = 1600

= ln (1600)

Rewrite

1600

in power-base form:

1600 = 4 0^{2}

= ln (4 0^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (4 0^{2}) = 2 ln (40)

= 2 ln (40)

ln (y) + ln (\frac{x}{y} + 1)

ln ∣ x ∣ + ln ∣ x - 1 ∣ + ln ∣ x + 1 ∣

ln ∣ b ∣ ln (\frac{b}{a}) + \frac{- ln ( ∣ b ∣ ^{2} ) + ln ( ∣ a ∣ ^{2} )}{2}

0 \cdot lo g_{10} (0.69) + (1 - 0) \cdot lo g_{10} (1 - 0.69)

lo g_{5} (\frac{1}{20})