What is simplify-log_{10}(3.2*10^{-3}) ?

The solution to simplify-log_{10}(3.2*10^{-3}) is -log_{10}(3.2)+3

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simplify-log_{10}(3.2*10^{-3})

simplify

- lo g_{10} (3.2 \cdot 1 0^{- 3})

- lo g_{10} (3.2) + 3

Decimal Notation

2.49485 \dots

Solution steps

- lo g_{10} (3.2 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (3.2 \cdot 1 0^{- 3}) = lo g_{10} (3.2) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (3.2) + 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} (3.2) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (3.2) - 3)

Distribute parentheses

= - (lo g_{10} (3.2)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (3.2) + 3

182000 \cdot [ln (0.63) - ln (1.3)]

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

lo g_{8} (3^{7}) + lo g_{8} (5^{7}) - lo g_{8} (1 6^{7})

4490 \cdot ln (\frac{( 23180 + 56088 )}{23180})

ln ((1 + i 3)^{2022})

What is simplify-log_{10}(3.2*10^{-3}) ?
The solution to simplify-log_{10}(3.2*10^{-3}) is -log_{10}(3.2)+3