What is simplify-log_{10}(4.6*10^{-3}) ?

The solution to simplify-log_{10}(4.6*10^{-3}) is -log_{10}(4.6)+3

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simplify-log_{10}(4.6*10^{-3})

simplify

- lo g_{10} (4.6 \cdot 1 0^{- 3})

- lo g_{10} (4.6) + 3

Decimal Notation

2.33724 \dots

Solution steps

- lo g_{10} (4.6 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (4.6 \cdot 1 0^{- 3}) = lo g_{10} (4.6) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (4.6) + 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} (4.6) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (4.6) - 3)

Distribute parentheses

= - (lo g_{10} (4.6)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (4.6) + 3

- ln (cos (x)) + ln (1 + sin (x))

ln (a b^{n})

ln (1 - x) + ln (1 + x)

ln (\frac{2 y ^{2}}{z ^{3}})

- 0.3 \cdot lo g_{2} (0.3) - 0.7 \cdot lo g_{2} (0.7)

What is simplify-log_{10}(4.6*10^{-3}) ?
The solution to simplify-log_{10}(4.6*10^{-3}) is -log_{10}(4.6)+3