What is ln((8n^2+1)/(n^2+1)) ?

The solution to ln((8n^2+1)/(n^2+1)) is ln(8n^2+1)-ln(n^2+1)

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simplify ln((8n^2+1)/(n^2+1))

simplify

ln (\frac{8 n ^{2} + 1}{n ^{2} + 1})

ln (8 n^{2} + 1) - ln (n^{2} + 1)

Solution steps

ln (\frac{8 n ^{2} + 1}{n ^{2} + 1})

Apply log rule:

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

ln (\frac{8 n ^{2} + 1}{n ^{2} + 1}) = ln (8 n^{2} + 1) - ln (n^{2} + 1)

= ln (8 n^{2} + 1) - ln (n^{2} + 1)

\frac{1}{4} lo g_{3} (2) + \frac{1}{4} lo g_{3} (x)

lo g_{2} (2 a)

3 ln (\frac{5}{7})

2 lo g_{3} (5) - lo g_{3} (2)

ln (\frac{x ^{8} p ^{7} q ^{9}}{e ^{9}})

What is ln((8n^2+1)/(n^2+1)) ?
The solution to ln((8n^2+1)/(n^2+1)) is ln(8n^2+1)-ln(n^2+1)