What is simplify-log_{10}(5.35*10^{-4}) ?

The solution to simplify-log_{10}(5.35*10^{-4}) is -log_{10}(5.35)+4

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simplify-log_{10}(5.35*10^{-4})

simplify

- lo g_{10} (5.35 \cdot 1 0^{- 4})

- lo g_{10} (5.35) + 4

Decimal Notation

3.27164 \dots

Solution steps

- lo g_{10} (5.35 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (5.35 \cdot 1 0^{- 4}) = lo g_{10} (5.35) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (5.35) + lo g_{10} (1 0^{- 4}))

Apply log rule:

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

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

= - (lo g_{10} (5.35) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (5.35) - 4)

Distribute parentheses

= - (lo g_{10} (5.35)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (5.35) + 4

7089.884206 \cdot ln (\frac{100 0 ^{2}}{4.5 \cdot 1 0 ^{8}})

ln (\frac{1}{0.5})

2 ln (x) + \frac{1}{2} ln (x^{2} - 4) - 3 ln (\frac{1}{x ^{2} + 2})

ln (7 (n + 1))

8 lo g_{6} (u) + 7 lo g_{6} (v)

What is simplify-log_{10}(5.35*10^{-4}) ?
The solution to simplify-log_{10}(5.35*10^{-4}) is -log_{10}(5.35)+4