What is simplify-log_{10}(7.5\times 10^{-6}) ?

The solution to simplify-log_{10}(7.5\times 10^{-6}) is -log_{10}(7.5)+6

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simplify-log_{10}(7.5\times 10^{-6})

simplify

- lo g_{10} (7.5 \cdot 1 0^{- 6})

- lo g_{10} (7.5) + 6

Decimal Notation

5.12493 \dots

Solution steps

- lo g_{10} (7.5 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (7.5 \cdot 1 0^{- 6}) = lo g_{10} (7.5) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (7.5) + lo g_{10} (1 0^{- 6}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 6}) = - 6 lo g_{10} (10)

= - (lo g_{10} (7.5) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (7.5) - 6)

Distribute parentheses

= - (lo g_{10} (7.5)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (7.5) + 6

lo g_{e} (3 x)

lo g_{4} (x^{7}) - lo g_{4} (x^{2}) + 4 lo g_{4} (x^{3})

lo g_{3} (2) - lo g_{3} (11)

lo g_{2} (x \cdot y \cdot z^{3})

- \frac{1}{3} lo g_{10} (\frac{1}{3}) - \frac{2}{3} lo g_{10} (\frac{2}{3})

What is simplify-log_{10}(7.5\times 10^{-6}) ?
The solution to simplify-log_{10}(7.5\times 10^{-6}) is -log_{10}(7.5)+6