What is simplify-log_{10}(7.5*10^{-3}) ?

The solution to simplify-log_{10}(7.5*10^{-3}) is -log_{10}(7.5)+3

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simplify-log_{10}(7.5*10^{-3})

simplify

- lo g_{10} (7.5 \cdot 1 0^{- 3})

- lo g_{10} (7.5) + 3

Decimal Notation

2.12493 \dots

Solution steps

- lo g_{10} (7.5 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (7.5 \cdot 1 0^{- 3}) = lo g_{10} (7.5) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (7.5) + 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} (7.5) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (7.5) - 3)

Distribute parentheses

= - (lo g_{10} (7.5)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (7.5) + 3

- lo g_{10} (4.3 \cdot 1 0^{- 7})

- \frac{5}{6} lo g_{2} (\frac{5}{6}) - \frac{1}{6} lo g_{2} (\frac{1}{6})

lo g_{10} (100000 x)

lo g_{9} (\frac{x ^{5}}{9})

2 lo g_{5} (x) + 3 lo g_{5} (y) - 8 lo g_{5} (z)

What is simplify-log_{10}(7.5*10^{-3}) ?
The solution to simplify-log_{10}(7.5*10^{-3}) is -log_{10}(7.5)+3