What is simplify-[10(ln(2)-ln(0.1))+5(2-0.1)] ?

The solution to simplify-[10(ln(2)-ln(0.1))+5(2-0.1)] is -10ln(20)-9.5

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simplify-[10(ln(2)-ln(0.1))+5(2-0.1)]

simplify

- [10 (ln (2) - ln (0.1)) + 5 (2 - 0.1)]

- 10 ln (20) - 9.5

Decimal Notation

- 39.45732 \dots

Solution steps

- [10 (ln (2) - ln (0.1)) + 5 (2 - 0.1)]

Apply log rule:

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

ln (2) - ln (0.1) = ln (\frac{2}{0.1})

= - [10 ln (\frac{2}{0.1}) + 5 (2 - 0.1)]

Divide the numbers:

\frac{2}{0.1} = 20

= - [10 ln (20) + 5 (2 - 0.1)]

5 (2 - 0.1) = 9.5

= - (10 ln (20) + 9.5)

Distribute parentheses

= - (10 ln (20)) - (9.5)

Apply minus-plus rules

+ (- a) = - a

= - 10 ln (20) - 9.5

ln (7) x - ln (7) - 2 ln (4)

0.3 5^{2} (ln (6.65) + 1.3 (ln (6.01) - ln (6.65)))

ln (\frac{1}{y} \cdot e^{- n θ})

9 lo g_{5} (x) + 3 lo g_{5} (y)

3 ln (\frac{1}{3}) - ln (\frac{1}{3})

What is simplify-[10(ln(2)-ln(0.1))+5(2-0.1)] ?
The solution to simplify-[10(ln(2)-ln(0.1))+5(2-0.1)] is -10ln(20)-9.5