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

The solution to ln((1+(-3)^2)/(1-(-3))) is ln(10)-2ln(2)

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

simplify

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

ln (10) - 2 ln (2)

Decimal Notation

0.91629 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply rule

- (- a) = a

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

ln (1 + (- 3)^{2}) = ln (10)

ln (1 + 3) = ln (4)

= ln (10) - ln (4)

ln (4) = 2 ln (2)

= ln (10) - 2 ln (2)

ln (\frac{1}{1 - 0.11})

ln (ab) - ln (a)

2 ln (\frac{u}{x})

lo g_{4} (\frac{- x}{x + 1})

ln (1 - x^{2}) + ln (a)

What is ln((1+(-3)^2)/(1-(-3))) ?
The solution to ln((1+(-3)^2)/(1-(-3))) is ln(10)-2ln(2)