What is simplify-log_{10}(1.09*10^{-3}) ?

The solution to simplify-log_{10}(1.09*10^{-3}) is -log_{10}(1.09)+3

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simplify-log_{10}(1.09*10^{-3})

simplify

- lo g_{10} (1.09 \cdot 1 0^{- 3})

- lo g_{10} (1.09) + 3

Decimal Notation

2.96257 \dots

Solution steps

- lo g_{10} (1.09 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.09 \cdot 1 0^{- 3}) = lo g_{10} (1.09) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (1.09) + 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} (1.09) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.09) - 3)

Distribute parentheses

= - (lo g_{10} (1.09)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.09) + 3

8.58 (1600 - 300) - (300 \cdot 8.58) ln (\frac{300}{1600})

\frac{1}{2} ln (x) + ln (c)

ln (\frac{2}{6})

lo g_{3} (2^{n})

ln (x (x - 6) (x + 3))

What is simplify-log_{10}(1.09*10^{-3}) ?
The solution to simplify-log_{10}(1.09*10^{-3}) is -log_{10}(1.09)+3