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

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

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simplify-log_{10}(1.8\times 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} (4 x)

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

lo g_{\frac{1}{4}} (16 z (x^{3} - 27))

- \frac{2}{3} lo g_{2} (\frac{2}{3}) - \frac{1}{3} lo g_{2} (\frac{1}{3})

2 (lo g_{5} (x) + 2 lo g_{5} (y) - 3 lo g_{5} (z))

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