What is simplify-log_{10}(5.08*10^{-5}) ?

The solution to simplify-log_{10}(5.08*10^{-5}) is -log_{10}(5.08)+5

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simplify-log_{10}(5.08*10^{-5})

simplify

- lo g_{10} (5.08 \cdot 1 0^{- 5})

- lo g_{10} (5.08) + 5

Decimal Notation

4.29413 \dots

Solution steps

- lo g_{10} (5.08 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (5.08 \cdot 1 0^{- 5}) = lo g_{10} (5.08) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (5.08) + lo g_{10} (1 0^{- 5}))

Apply log rule:

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

lo g_{10} (1 0^{- 5}) = - 5 lo g_{10} (10)

= - (lo g_{10} (5.08) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (5.08) - 5)

Distribute parentheses

= - (lo g_{10} (5.08)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (5.08) + 5

2.45 + lo g_{10} (\frac{0.047}{0.054})

ln (x) + \frac{2}{5} ln (5 u^{2} + 1)

- 9 ln (9 x) - (\frac{1}{9}) ln (2700 - 9 x)

ln (3000) - ln (2000)

lo g_{4} (\frac{1}{42})

What is simplify-log_{10}(5.08*10^{-5}) ?
The solution to simplify-log_{10}(5.08*10^{-5}) is -log_{10}(5.08)+5