What is simplify-ln(1.5*10^{-3}) ?

The solution to simplify-ln(1.5*10^{-3}) is -ln(1.5)+3ln(10)

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simplify-ln(1.5*10^{-3})

simplify

- ln (1.5 \cdot 1 0^{- 3})

- ln (1.5) + 3 ln (10)

Decimal Notation

6.50229 \dots

Solution steps

- ln (1.5 \cdot 1 0^{- 3})

Apply log rule:

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

ln (1.5 \cdot 1 0^{- 3}) = ln (1.5) + ln (1 0^{- 3})

= - (ln (1.5) + ln (1 0^{- 3}))

Apply log rule:

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

ln (1 0^{- 3}) = - 3 ln (10)

= - (ln (1.5) - 3 ln (10))

Distribute parentheses

= - (ln (1.5)) - (- 3 ln (10))

Apply minus-plus rules

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

= - ln (1.5) + 3 ln (10)

lo g_{10} (- 4 i)

0.065 \cdot ln (\frac{5}{150})

ln (3.9) - ln (2.91)

ln (f (x) \cdot g (x))

lo g_{10} (x y)

What is simplify-ln(1.5*10^{-3}) ?
The solution to simplify-ln(1.5*10^{-3}) is -ln(1.5)+3ln(10)