What is simplify-ln(1.8*10^{-5}) ?

The solution to simplify-ln(1.8*10^{-5}) is -ln(1.8)+5ln(10)

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simplify-ln(1.8*10^{-5})

simplify

- ln (1.8 \cdot 1 0^{- 5})

- ln (1.8) + 5 ln (10)

Decimal Notation

10.92513 \dots

Solution steps

- ln (1.8 \cdot 1 0^{- 5})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (1.8 \cdot 1 0^{- 5}) = ln (1.8) + ln (1 0^{- 5})

= - (ln (1.8) + ln (1 0^{- 5}))

Apply log rule:

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

ln (1 0^{- 5}) = - 5 ln (10)

= - (ln (1.8) - 5 ln (10))

Distribute parentheses

= - (ln (1.8)) - (- 5 ln (10))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - ln (1.8) + 5 ln (10)

4 ln (5 x)

ln (\frac{1}{140})

4 ln (x) - ln (v^{4} + 1)

2 \cdot ln (- 2) - 2 \cdot ln (2)

ln (\frac{4}{10000})

What is simplify-ln(1.8*10^{-5}) ?
The solution to simplify-ln(1.8*10^{-5}) is -ln(1.8)+5ln(10)