What is simplify-ln(3.02*10^{-8}) ?

The solution to simplify-ln(3.02*10^{-8}) is -ln(3.02)+8ln(10)

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simplify-ln(3.02*10^{-8})

simplify

- ln (3.02 \cdot 1 0^{- 8})

- ln (3.02) + 8 ln (10)

Decimal Notation

17.31542 \dots

Solution steps

- ln (3.02 \cdot 1 0^{- 8})

Apply log rule:

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

ln (3.02 \cdot 1 0^{- 8}) = ln (3.02) + ln (1 0^{- 8})

= - (ln (3.02) + ln (1 0^{- 8}))

Apply log rule:

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

ln (1 0^{- 8}) = - 8 ln (10)

= - (ln (3.02) - 8 ln (10))

Distribute parentheses

= - (ln (3.02)) - (- 8 ln (10))

Apply minus-plus rules

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

= - ln (3.02) + 8 ln (10)

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What is simplify-ln(3.02*10^{-8}) ?
The solution to simplify-ln(3.02*10^{-8}) is -ln(3.02)+8ln(10)