What is simplify-log_{10}(1.3*10^{-3}) ?

The solution to simplify-log_{10}(1.3*10^{-3}) is -log_{10}(1.3)+3

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simplify-log_{10}(1.3*10^{-3})

simplify

- lo g_{10} (1.3 \cdot 1 0^{- 3})

- lo g_{10} (1.3) + 3

Decimal Notation

2.88605 \dots

Solution steps

- lo g_{10} (1.3 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.3 \cdot 1 0^{- 3}) = lo g_{10} (1.3) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (1.3) + 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} (1.3) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (1.3) - 3)

Distribute parentheses

= - (lo g_{10} (1.3)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.3) + 3

2 lo g_{a} (3) + lo g_{a} (5)

2 [lo g_{a} (x) - lo g_{a} (y + 1) + lo g_{a} (z)]

lo g_{2} (\frac{4}{x + 4})

ln (x) + 4 ln (y)

ln (x) + 2 ln (y)

What is simplify-log_{10}(1.3*10^{-3}) ?
The solution to simplify-log_{10}(1.3*10^{-3}) is -log_{10}(1.3)+3