What is simplify-log_{10}(3.6e^{-13}) ?

The solution to simplify-log_{10}(3.6e^{-13}) is -log_{10}(3.6)+13log_{10}(e)

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simplify-log_{10}(3.6e^{-13})

simplify

- lo g_{10} (3.6 e^{- 13})

- lo g_{10} (3.6) + 13 lo g_{10} (e)

Decimal Notation

5.08952 \dots

Solution steps

- lo g_{10} (3.6 e^{- 13})

Apply log rule:

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

lo g_{10} (3.6 e^{- 13}) = lo g_{10} (3.6) + lo g_{10} (e^{- 13})

= - (lo g_{10} (3.6) + lo g_{10} (e^{- 13}))

Apply log rule:

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

lo g_{10} (e^{- 13}) = - 13 lo g_{10} (e)

= - (lo g_{10} (3.6) - 13 lo g_{10} (e))

Distribute parentheses

= - (lo g_{10} (3.6)) - (- 13 lo g_{10} (e))

Apply minus-plus rules

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

= - lo g_{10} (3.6) + 13 lo g_{10} (e)

ln (7.83) - 6 ln (10)

\frac{ln ( 36731 ) - ln ( 27682 )}{2021 - 2000}

2 ln (2 + 1) + ln (2 + 1) + 1 - 2 - 2 ln (2)

ln (\frac{x ^{3}}{8})

4 ln (3) - 5 ln (z - 6)

What is simplify-log_{10}(3.6e^{-13}) ?
The solution to simplify-log_{10}(3.6e^{-13}) is -log_{10}(3.6)+13log_{10}(e)