What is simplify-log_{10}(5*10^{-7}) ?

The solution to simplify-log_{10}(5*10^{-7}) is -log_{10}(5)+7

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simplify-log_{10}(5*10^{-7})

simplify

- lo g_{10} (5 \cdot 1 0^{- 7})

- lo g_{10} (5) + 7

Decimal Notation

6.30102 \dots

Solution steps

- lo g_{10} (5 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (5 \cdot 1 0^{- 7}) = lo g_{10} (5) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (5) + 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) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (5) - 7)

Distribute parentheses

= - (lo g_{10} (5)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (5) + 7

2 lo g_{4} (5) + 2 lo g_{4} (11) + lo g_{4} (6)

ln (\frac{6}{e})

lo g_{2} (2) + lo g_{2} (9) + lo g_{2} (6)

ln ∣ 7 - 2 ∣ - \frac{3}{2} ln ∣ 2 \cdot 7 - 1 ∣ + 2 ln ∣ 7 + 3 ∣

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

What is simplify-log_{10}(5*10^{-7}) ?
The solution to simplify-log_{10}(5*10^{-7}) is -log_{10}(5)+7