What is ln(([0.2]^1)/([0.1]^2)) ?

The solution to ln(([0.2]^1)/([0.1]^2)) is ln(0.2)-2ln(0.1)

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simplify ln(([0.2]^1)/([0.1]^2))

simplify

ln (\frac{[ 0.2 ] ^{1}}{[ 0.1 ] ^{2}})

ln (0.2) - 2 ln (0.1)

Decimal Notation

2.99573 \dots

Solution steps

ln (\frac{[ 0.2 ] ^{1}}{[ 0.1 ] ^{2}})

Apply log rule:

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

ln (\frac{[ 0.2 ] ^{1}}{[ 0.1 ] ^{2}}) = ln ([0.2]^{1}) - ln ([0.1]^{2})

= ln ([0.2]^{1}) - ln ([0.1]^{2})

Apply log rule:

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

ln ([0.2]^{1}) = 1 \cdot ln (0.2)

= 1 \cdot ln (0.2) - ln ([0.1]^{2})

Apply log rule:

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

ln ([0.1]^{2}) = 2 ln (0.1)

= 1 \cdot ln (0.2) - 2 ln (0.1)

Multiply:

1 \cdot ln (0.2) = ln (0.2)

= ln (0.2) - 2 ln (0.1)

lo g_{10} (\frac{10000}{y})

lo g_{2} (3) + lo g_{2} (6) - lo g_{2} (4)

3 (2 lo g_{10} (2 A) - 5 lo g_{10} (2 B))

ln (\frac{6 + 0.5}{7 \cdot 0.5})

\frac{1}{9} ln (\frac{6}{5})

What is ln(([0.2]^1)/([0.1]^2)) ?
The solution to ln(([0.2]^1)/([0.1]^2)) is ln(0.2)-2ln(0.1)