What is log_{10}(1/(5.25*10^{-8)}) ?

The solution to log_{10}(1/(5.25*10^{-8)}) is -(log_{10}(5.25)-8)

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simplify log_{10}(1/(5.25*10^{-8)})

simplify

lo g_{10} (\frac{1}{5.25 \cdot 1 0 ^{- 8}})

- (lo g_{10} (5.25) - 8)

Decimal Notation

7.27984 \dots

Solution steps

lo g_{10} (\frac{1}{5.25 \cdot 1 0 ^{- 8}})

Apply log rule:

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

lo g_{10} (\frac{1}{5.25 \cdot 1 0 ^{- 8}}) = lo g_{10} (1) - lo g_{10} (5.25 \cdot 1 0^{- 8})

= lo g_{10} (1) - lo g_{10} (1 0^{- 8} \cdot 5.25)

Apply log rule:

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

lo g_{10} (5.25 \cdot 1 0^{- 8}) = lo g_{10} (5.25) + lo g_{10} (1 0^{- 8})

= lo g_{10} (1) - (lo g_{10} (5.25) + lo g_{10} (1 0^{- 8}))

Apply log rule:

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

lo g_{10} (1 0^{- 8}) = - 8 lo g_{10} (10)

= lo g_{10} (1) - (lo g_{10} (5.25) - 8 lo g_{10} (10))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (lo g_{10} (5.25) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= 0 - (lo g_{10} (5.25) - 8)

0 - (lo g_{10} (5.25) - 8) = - (lo g_{10} (5.25) - 8)

= - (lo g_{10} (5.25) - 8)

2500 - (ln (x^{2} + 6 x + 9) - ln (x + 3))

ln (A e^{- t})

lo g_{e} (3^{\frac{1}{6}}) + lo g_{e} (6^{\frac{1}{3}})

\frac{2}{3} ln (x - 2) - 2 ln (x + 1) + ln (2 x)

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

What is log_{10}(1/(5.25*10^{-8)}) ?
The solution to log_{10}(1/(5.25*10^{-8)}) is -(log_{10}(5.25)-8)