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

The solution to ln((3^2+1)/(2(3)^2+1)) is ln(10)-ln(19)

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

simplify

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

ln (10) - ln (19)

Decimal Notation

- 0.64185 \dots

Solution steps

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

Apply log rule:

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

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

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

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

ln (2 \cdot 3^{2} + 1) = ln (19)

= ln (10) - ln (19)

ln (5) - ln (11)

ln ((x + 61)^{0.5} (x - 11)^{0.5})

ln (\frac{83}{95})

ln (x^{2} - 6 x - 16) - ln (x + 2)

ln (\frac{x ^{2}}{8})

What is ln((3^2+1)/(2(3)^2+1)) ?
The solution to ln((3^2+1)/(2(3)^2+1)) is ln(10)-ln(19)