What is ln(1+sqrt(0.999))-ln(0.999) ?

The solution to ln(1+sqrt(0.999))-ln(0.999) is ln(2.00150…)

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simplify ln(1+sqrt(0.999))-ln(0.999)

simplify

ln (1 + 0.999) - ln (0.999)

ln (2.00150 \dots)

Decimal Notation

0.69389 \dots

Solution steps

ln (1 + 0.999) - ln (0.999)

Apply log rule:

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

ln (1 + 0.999) - ln (0.999) = ln (\frac{1 + 0.999}{0.999})

= ln (\frac{1 + 0.999}{0.999})

\frac{1 + 0.999}{0.999} = 2.00150 \dots

= ln (2.00150 \dots)

ln (0.1 + 0.5) - ln (0.5)

ln (\frac{2 \cdot 3}{3})

ln (\frac{51.104}{47.2})

ln (- 1 (1))

ln (\frac{\frac{1}{a}}{a})

What is ln(1+sqrt(0.999))-ln(0.999) ?
The solution to ln(1+sqrt(0.999))-ln(0.999) is ln(2.00150…)