What is simplify-log_{10}(3.52(10^{-3})) ?

The solution to simplify-log_{10}(3.52(10^{-3})) is -log_{10}(3.52)+3

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simplify-log_{10}(3.52(10^{-3}))

simplify

- lo g_{10} (3.52 (1 0^{- 3}))

- lo g_{10} (3.52) + 3

Decimal Notation

2.45345 \dots

Solution steps

- lo g_{10} (3.52 (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (3.52 (1 0^{- 3})) = lo g_{10} (3.52) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (3.52) + lo g_{10} (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= - (lo g_{10} (3.52) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (3.52) - 3)

Distribute parentheses

= - (lo g_{10} (3.52)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (3.52) + 3

5 ln (x^{2}) + ln (9 x)

- ln (\frac{65}{75})

ln (\frac{0.53}{12})

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

ln (D e^{- \frac{q}{r t}})

What is simplify-log_{10}(3.52(10^{-3})) ?
The solution to simplify-log_{10}(3.52(10^{-3})) is -log_{10}(3.52)+3