What is simplify-log_{10}(1.6*10^{-7}) ?

The solution to simplify-log_{10}(1.6*10^{-7}) is -log_{10}(1.6)+7

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simplify-log_{10}(1.6*10^{-7})

simplify

- lo g_{10} (1.6 \cdot 1 0^{- 7})

- lo g_{10} (1.6) + 7

Decimal Notation

6.79588 \dots

Solution steps

- lo g_{10} (1.6 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (1.6 \cdot 1 0^{- 7}) = lo g_{10} (1.6) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (1.6) + 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} (1.6) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (1.6) - 7)

Distribute parentheses

= - (lo g_{10} (1.6)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (1.6) + 7

5 lo g_{10} (x) + 7 lo g_{10} (y)

lo g_{10} (\frac{6 x}{y})

ln (\frac{( e ^{x l n (2)} )}{2})

lo g_{5} (6) + lo g_{5} (7)

lo g_{10} (2 x^{4})

What is simplify-log_{10}(1.6*10^{-7}) ?
The solution to simplify-log_{10}(1.6*10^{-7}) is -log_{10}(1.6)+7