What is simplify-log_{10}(4.1*10^{-3}) ?

The solution to simplify-log_{10}(4.1*10^{-3}) is -log_{10}(4.1)+3

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simplify-log_{10}(4.1*10^{-3})

simplify

- lo g_{10} (4.1 \cdot 1 0^{- 3})

- lo g_{10} (4.1) + 3

Decimal

2.38721 \dots

Solution steps

- lo g_{10} (4.1 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (4.1 \cdot 1 0^{- 3}) = lo g_{10} (4.1) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (4.1) + 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} (4.1) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (4.1) - 3)

Distribute parentheses

= - (lo g_{10} (4.1)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (4.1) + 3

4 lo g_{10} (3 x^{3}) - \frac{1}{2} lo g_{10} (9 x^{8})

lo g_{10} (81) - lo g_{10} (\frac{64}{36})

5 ln (a) + \frac{ln ( b )}{3} - 3 ln (c)

ln (\frac{1}{72})

lo g_{10} (x) - \frac{1}{2} lo g_{10} (y) + 3 lo g_{10} (z)

What is simplify-log_{10}(4.1*10^{-3}) ?
The solution to simplify-log_{10}(4.1*10^{-3}) is -log_{10}(4.1)+3