What is log_{10}(((4*10^{-7}))/((1*10^{-12))}) ?

The solution to log_{10}(((4*10^{-7}))/((1*10^{-12))}) is 2log_{10}(2)+5

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simplify log_{10}(((410^{-7}))/((110^{-12))})

simplify

lo g_{10} (\frac{( 4 \cdot 1 0 ^{- 7} )}{( 1 \cdot 1 0 ^{- 12} )})

2 lo g_{10} (2) + 5

Decimal Notation

5.60205 \dots

Solution steps

lo g_{10} (\frac{( 4 \cdot 1 0 ^{- 7} )}{( 1 \cdot 1 0 ^{- 12} )})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{( 4 \cdot 1 0 ^{- 7} )}{( 1 \cdot 1 0 ^{- 12} )}) = lo g_{10} ((4 \cdot 1 0^{- 7})) - lo g_{10} ((1 \cdot 1 0^{- 12}))

= lo g_{10} (1 0^{- 7} \cdot 4) - lo g_{10} (1 0^{- 12} \cdot 1)

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} (1 \cdot 1 0^{- 12}) = lo g_{10} (1) + lo g_{10} (1 0^{- 12})

= lo g_{10} (4) + lo g_{10} (1 0^{- 7}) - (lo g_{10} (1) + lo g_{10} (1 0^{- 12}))

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) - (lo g_{10} (1) + lo g_{10} (1 0^{- 12}))

Apply log rule:

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

lo g_{10} (1 0^{- 12}) = - 12 lo g_{10} (10)

= lo g_{10} (4) - 7 lo g_{10} (10) - (lo g_{10} (1) - 12 lo g_{10} (10))

7 lo g_{10} (10) = 7

- (lo g_{10} (1) - 12 lo g_{10} (10)) = 12

= lo g_{10} (4) - 7 + 12

Add/Subtract the numbers:

- 7 + 12 = 5

= lo g_{10} (4) + 5

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

= 2 lo g_{10} (2) + 5

ln (p^{x} (1 - p)^{1 - x})

4 lo g_{10} (x) - 9 lo g_{10} (y)

3 lo g_{a} (x + y) - 2 lo g_{a} (x - y)

\frac{ln ( x )}{2} + ln (3 - x) - ln (2)

ln (7 - 3) - ln (2 - 3)

What is log_{10}(((4*10^{-7}))/((1*10^{-12))}) ?
The solution to log_{10}(((4*10^{-7}))/((1*10^{-12))}) is 2log_{10}(2)+5