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

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

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

simplify

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

ln (2) - ln (3)

Decimal Notation

- 0.40546 \dots

Solution steps

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

Apply log rule:

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

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

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

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

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

= ln (2) - ln (3)

ln (\frac{400}{300})

- \frac{1}{9} ln (3)

40 e^{9} - 15 ln (19) + 210 + 15 ln (x)

- lo g_{10} (1.09 \cdot 1 0^{- 3})

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