What is simplify-log_{10}(1.8*10^{-5}) ?

The solution to simplify-log_{10}(1.8*10^{-5}) is -log_{10}(1.8)+5

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simplify-log_{10}(1.8*10^{-5})

simplify

- lo g_{10} (1.8 \cdot 1 0^{- 5})

- lo g_{10} (1.8) + 5

Decimal Notation

4.74472 \dots

Solution steps

- lo g_{10} (1.8 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (1.8 \cdot 1 0^{- 5}) = lo g_{10} (1.8) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (1.8) + 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} (1.8) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (1.8) - 5)

Distribute parentheses

= - (lo g_{10} (1.8)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (1.8) + 5

lo g_{10} (\frac{10 a 0.1}{10})

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

What is simplify-log_{10}(1.8*10^{-5}) ?
The solution to simplify-log_{10}(1.8*10^{-5}) is -log_{10}(1.8)+5