What is simplify-log_{10}(5*10^{-3}) ?

The solution to simplify-log_{10}(5*10^{-3}) is -log_{10}(5)+3

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simplify-log_{10}(5*10^{-3})

simplify

- lo g_{10} (5 \cdot 1 0^{- 3})

- lo g_{10} (5) + 3

Decimal Notation

2.30102 \dots

Solution steps

- lo g_{10} (5 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (5 \cdot 1 0^{- 3}) = lo g_{10} (5) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (5) + 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} (5) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (5) - 3)

Distribute parentheses

= - (lo g_{10} (5)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (5) + 3

2 ln (x) + 3 ln (y) - 5 ln (z)

ln (x^{9}) - \frac{1}{4} ln (x^{- 7})

6 ln (x) + 4 ln (y) - 2 ln (z)

lo g_{4} (\frac{2 x + 1}{3 y + 4})

What is simplify-log_{10}(5*10^{-3}) ?
The solution to simplify-log_{10}(5*10^{-3}) is -log_{10}(5)+3