What is ln((5^2)/(5^2+(-5)^2)) ?

The solution to ln((5^2)/(5^2+(-5)^2)) is 2ln(5)-ln(50)

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simplify ln((5^2)/(5^2+(-5)^2))

simplify

ln (\frac{5 ^{2}}{5 ^{2} + ( - 5 ) ^{2}})

2 ln (5) - ln (50)

Decimal Notation

- 0.69314 \dots

Solution steps

ln (\frac{5 ^{2}}{5 ^{2} + ( - 5 ) ^{2}})

Apply log rule:

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

ln (\frac{5 ^{2}}{5 ^{2} + ( - 5 ) ^{2}}) = ln (5^{2}) - ln (5^{2} + (- 5)^{2})

= ln (5^{2}) - ln (5^{2} + (- 5)^{2})

Apply log rule:

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

ln (5^{2}) = 2 ln (5)

= 2 ln (5) - ln (5^{2} + (- 5)^{2})

ln (5^{2} + (- 5)^{2}) = ln (50)

= 2 ln (5) - ln (50)

\frac{2}{3} lo g_{8} (7) - lo g_{8} (5)

(\frac{1}{e})^{2} lo g_{7} (\frac{1}{e})

ln (\frac{r}{4 s})

0.4 \cdot lo g_{2} (0.4) + 0.6 \cdot lo g_{2} (0.6)

lo g_{3} (11) - lo g_{3} (2)

What is ln((5^2)/(5^2+(-5)^2)) ?
The solution to ln((5^2)/(5^2+(-5)^2)) is 2ln(5)-ln(50)