What is simplify-log_{10}(5.66*10^{-7}) ?

The solution to simplify-log_{10}(5.66*10^{-7}) is -log_{10}(5.66)+7

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simplify-log_{10}(5.66*10^{-7})

simplify

- lo g_{10} (5.66 \cdot 1 0^{- 7})

- lo g_{10} (5.66) + 7

Decimal Notation

6.24718 \dots

Solution steps

- lo g_{10} (5.66 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (5.66 \cdot 1 0^{- 7}) = lo g_{10} (5.66) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (5.66) + lo g_{10} (1 0^{- 7}))

Apply log rule:

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

lo g_{10} (1 0^{- 7}) = - 7 lo g_{10} (10)

= - (lo g_{10} (5.66) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (5.66) - 7)

Distribute parentheses

= - (lo g_{10} (5.66)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (5.66) + 7

- (\frac{7}{9} lo g_{2} (\frac{7}{9}) + \frac{2}{9} lo g_{2} (\frac{2}{9}))

lo g_{5} (7) + 4 lo g_{5} (x)

ln (\frac{x ^{2}}{x + 5})

ln (\frac{a}{b}) - 3 ln (a^{2}) + ln (b^{- 2})

3 lo g_{6} (u) + 7 lo g_{6} (v)

What is simplify-log_{10}(5.66*10^{-7}) ?
The solution to simplify-log_{10}(5.66*10^{-7}) is -log_{10}(5.66)+7