What is ln((1+(10)^2)*(-20)^2) ?

The solution to ln((1+(10)^2)*(-20)^2) is ln(101)+2ln(-20)

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simplify ln((1+(10)^2)*(-20)^2)

simplify

ln ((1 + (10)^{2}) \cdot (- 20)^{2})

ln (101) + 2 ln (- 20)

Solution steps

ln ((1 + (10)^{2}) (- 20)^{2})

Apply log rule:

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

ln ((1 + 1 0^{2}) (- 20)^{2}) = ln (1 + 1 0^{2}) + ln ((- 20)^{2})

= ln (1 0^{2} + 1) + ln ((- 20)^{2})

Apply log rule:

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

ln ((- 20)^{2}) = 2 ln (- 20)

= ln (1 + 1 0^{2}) + 2 ln (- 20)

ln (1 + 1 0^{2}) = ln (101)

= ln (101) + 2 ln (- 20)

ln (x) - \frac{1}{4} ln (y)

- lo g_{10} (1.7 (1 0^{- 9}))

182000 (ln (0.44) - ln (1.3))

3.74 + lo g_{10} (\frac{0.0005}{0.0495})

- ln (t + 60) + ln (60)

What is ln((1+(10)^2)*(-20)^2) ?
The solution to ln((1+(10)^2)*(-20)^2) is ln(101)+2ln(-20)