What is ln(ln(1/(1-0.02)))-ln(ln(1/(1-0.003))) ?

The solution to ln(ln(1/(1-0.02)))-ln(ln(1/(1-0.003))) is ln(6.72412…)

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simplify ln(ln(1/(1-0.02)))-ln(ln(1/(1-0.003)))

simplify

ln (ln (\frac{1}{1 - 0.02})) - ln (ln (\frac{1}{1 - 0.003}))

ln (6.72412 \dots)

Decimal Notation

1.90570 \dots

Solution steps

ln (ln (\frac{1}{1 - 0.02})) - ln (ln (\frac{1}{1 - 0.003}))

Apply log rule:

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

ln (ln (\frac{1}{1 - 0.02})) - ln (ln (\frac{1}{1 - 0.003})) = ln (\frac{ln ( \frac{1}{1 - 0.02} )}{ln ( \frac{1}{1 - 0.003} )})

= ln (\frac{ln ( \frac{1}{1 - 0.02} )}{ln ( \frac{1}{1 - 0.003} )})

\frac{ln ( \frac{1}{1 - 0.02} )}{ln ( \frac{1}{1 - 0.003} )} = 6.72412 \dots

= ln (6.72412 \dots)

2.45 + lo g_{10} (\frac{0.022}{0.069})

(0.287) ln (\frac{500}{200})

2 lo g_{3} (2) - 3 lo g_{3} (4) - 2 lo g_{3} (5)

ln (19) - ln (44)

ln (0.5833) - ln (1.625)

What is ln(ln(1/(1-0.02)))-ln(ln(1/(1-0.003))) ?
The solution to ln(ln(1/(1-0.02)))-ln(ln(1/(1-0.003))) is ln(6.72412…)