What is ln((0.015^2)/(0.011^2)) ?

The solution to ln((0.015^2)/(0.011^2)) is 2ln(0.015)-2ln(0.011)

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simplify ln((0.015^2)/(0.011^2))

simplify

ln (\frac{0.01 5 ^{2}}{0.01 1 ^{2}})

2 ln (0.015) - 2 ln (0.011)

Decimal Notation

0.62030 \dots

Solution steps

ln (\frac{0.01 5 ^{2}}{0.01 1 ^{2}})

Apply log rule:

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

ln (\frac{0.01 5 ^{2}}{0.01 1 ^{2}}) = ln (0.01 5^{2}) - ln (0.01 1^{2})

= ln (0.01 5^{2}) - ln (0.01 1^{2})

Apply log rule:

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

ln (0.01 5^{2}) = 2 ln (0.015)

= 2 ln (0.015) - ln (0.01 1^{2})

Apply log rule:

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

ln (0.01 1^{2}) = 2 ln (0.011)

= 2 ln (0.015) - 2 ln (0.011)

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What is ln((0.015^2)/(0.011^2)) ?
The solution to ln((0.015^2)/(0.011^2)) is 2ln(0.015)-2ln(0.011)