What is simplify-log_{10}(0.6(10^{-3})) ?

The solution to simplify-log_{10}(0.6(10^{-3})) is -log_{10}(0.6)+3

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simplify-log_{10}(0.6(10^{-3}))

simplify

- lo g_{10} (0.6 (1 0^{- 3}))

- lo g_{10} (0.6) + 3

Decimal Notation

3.22184 \dots

Solution steps

- lo g_{10} (0.6 (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (0.6 (1 0^{- 3})) = lo g_{10} (0.6) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (0.6) + lo g_{10} (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= - (lo g_{10} (0.6) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (0.6) - 3)

Distribute parentheses

= - (lo g_{10} (0.6)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (0.6) + 3

ln (12 \frac{12}{5})

10 lo g_{10} (56.27) - 10 lo g_{10} (33.52)

ln (\frac{11}{0.5})

\frac{1}{16} ln (\frac{18}{10})

\frac{ln ( 18677 ) - ln ( 100 )}{ln ( 75000 ) - ln ( 100 )}

What is simplify-log_{10}(0.6(10^{-3})) ?
The solution to simplify-log_{10}(0.6(10^{-3})) is -log_{10}(0.6)+3