What is simplify-log_{10}(4.2\times 10^{-3}) ?

The solution to simplify-log_{10}(4.2\times 10^{-3}) is -log_{10}(4.2)+3

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simplify-log_{10}(4.2\times 10^{-3})

simplify

- lo g_{10} (4.2 \cdot 1 0^{- 3})

- lo g_{10} (4.2) + 3

Decimal Notation

2.37675 \dots

Solution steps

- lo g_{10} (4.2 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (4.2 \cdot 1 0^{- 3}) = lo g_{10} (4.2) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (4.2) + 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} (4.2) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (4.2) - 3)

Distribute parentheses

= - (lo g_{10} (4.2)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (4.2) + 3

- ln (x + 2) + 2 ln (x + 3)

2 lo g_{5} (3 x + 2) - lo g_{5} (x + 1)

lo g_{3} (x (x + 1))

lo g_{5} (2 x)

lo g_{10} (z^{9} y)

What is simplify-log_{10}(4.2\times 10^{-3}) ?
The solution to simplify-log_{10}(4.2\times 10^{-3}) is -log_{10}(4.2)+3