What is simplify-log_{10}(4*10^{-7}) ?

The solution to simplify-log_{10}(4*10^{-7}) is -2log_{10}(2)+7

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simplify-log_{10}(4*10^{-7})

simplify

- lo g_{10} (4 \cdot 1 0^{- 7})

- 2 lo g_{10} (2) + 7

Decimal Notation

6.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 7}) = lo g_{10} (4) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (4) + 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} (4) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (4) - 7)

lo g_{10} (4) = 2 lo g_{10} (2)

= - (2 lo g_{10} (2) - 7)

Distribute parentheses

= - (2 lo g_{10} (2)) - (- 7)

Apply minus-plus rules

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

= - 2 lo g_{10} (2) + 7

ln (\frac{e ^{2} - e ^{4} - 1}{2 - 5})

- lo g_{10} (2.14 \cdot 1 0^{- 2})

- 5 ln (\frac{0.01}{0.9})

lo g_{7} (13.3) - lo g_{7} (1.9)

What is simplify-log_{10}(4*10^{-7}) ?
The solution to simplify-log_{10}(4*10^{-7}) is -2log_{10}(2)+7