What is 2ln(10)-1/2 ln(1.001) ?

The solution to 2ln(10)-1/2 ln(1.001) is ln(99.95003…)

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simplify 2ln(10)-1/2 ln(1.001)

simplify

2 ln (10) - \frac{1}{2} ln (1.001)

ln (99.95003 \dots)

Decimal Notation

4.60467 \dots

Solution steps

2 ln (10) - \frac{1}{2} ln (1.001)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (10) = ln (1 0^{2})

= ln (1 0^{2}) - \frac{1}{2} ln (1.001)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (1.001) = ln (1.00 1^{\frac{1}{2}})

= ln (1 0^{2}) - ln (1.00 1^{\frac{1}{2}})

Apply log rule:

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

ln (1 0^{2}) - ln (1.00 1^{\frac{1}{2}}) = ln (\frac{1 0 ^{2}}{1.00 1 ^{\frac{1}{2}}})

= ln (\frac{1 0 ^{2}}{1.00 1 ^{\frac{1}{2}}})

\frac{1 0 ^{2}}{1.00 1 ^{\frac{1}{2}}} = 99.95003 \dots

= ln (99.95003 \dots)

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ln (9000 e^{9})

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What is 2ln(10)-1/2 ln(1.001) ?
The solution to 2ln(10)-1/2 ln(1.001) is ln(99.95003…)