What is simplify-log_{10}(4.55*10^{-8}) ?

The solution to simplify-log_{10}(4.55*10^{-8}) is -log_{10}(4.55)+8

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simplify-log_{10}(4.55*10^{-8})

simplify

- lo g_{10} (4.55 \cdot 1 0^{- 8})

- lo g_{10} (4.55) + 8

Decimal Notation

7.34198 \dots

Solution steps

- lo g_{10} (4.55 \cdot 1 0^{- 8})

Apply log rule:

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

lo g_{10} (4.55 \cdot 1 0^{- 8}) = lo g_{10} (4.55) + lo g_{10} (1 0^{- 8})

= - (lo g_{10} (4.55) + 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} (4.55) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (4.55) - 8)

Distribute parentheses

= - (lo g_{10} (4.55)) - (- 8)

Apply minus-plus rules

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

= - lo g_{10} (4.55) + 8

- \frac{1}{6} \cdot lo g_{2} (\frac{1}{6}) - \frac{5}{6} \cdot lo g_{2} (\frac{5}{6})

5 ln (x + 4) - 8 ln (x)

\frac{1}{3} (ln (x) + ln (y)) - 4 ln (z)

10 lo g_{10} (\frac{1}{86400} (1 0^{\frac{115}{10}}))

ln (\frac{19.738}{1.9738})

What is simplify-log_{10}(4.55*10^{-8}) ?
The solution to simplify-log_{10}(4.55*10^{-8}) is -log_{10}(4.55)+8