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

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

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

simplify

- ln (1.8 \cdot 10 e^{- 5})

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

Decimal Notation

2.10962 \dots

Solution steps

- ln (1.8 \cdot 10 e^{- 5})

Apply log rule:

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

ln (1.8 \cdot 10 e^{- 5}) = ln (1.8) + ln (10) + ln (e^{- 5})

= - (ln (10) + ln (1.8) + ln (e^{- 5}))

Apply log rule:

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

ln (e^{- 5}) = - 5 ln (e)

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

5 ln (e) = 5

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

Distribute parentheses

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

Apply minus-plus rules

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

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

\frac{2}{5} ln (2)

ln ((x - 4)^{4} (x - 6))

ln (ab) + 2 ln (ab)

\frac{1}{2} ln (a x)

\frac{ln ( 4 )}{- ln ( 4 ) - 2 ln ( 3 )}

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