What is simplify-log_{10}(7.5*10^{-3})+log_{10}(3) ?

The solution to simplify-log_{10}(7.5*10^{-3})+log_{10}(3) is 2log_{10}(20)

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simplify-log_{10}(7.5*10^{-3})+log_{10}(3)

simplify

- lo g_{10} (7.5 \cdot 1 0^{- 3}) + lo g_{10} (3)

2 lo g_{10} (20)

Decimal Notation

2.60205 \dots

Solution steps

- lo g_{10} (7.5 \cdot 1 0^{- 3}) + lo g_{10} (3)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (3) - lo g_{10} (7.5 \cdot 1 0^{- 3}) = lo g_{10} (\frac{3}{7.5 \cdot 1 0 ^{- 3}})

= lo g_{10} (\frac{3}{7.5 \cdot 1 0 ^{- 3}})

\frac{3}{7.5 \cdot 1 0 ^{- 3}} = 400

= lo g_{10} (400)

Factor the number:

400 = 2 0^{2}

= lo g_{10} (2 0^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (2 0^{2}) = 2 lo g_{10} (20)

= 2 lo g_{10} (20)

\frac{1}{2} lo g_{10} (8 + 65)

ln (13) + 7 ln (a) - 11 ln (b) + ln (c)

lo g_{10} (0.48 5^{\frac{1}{4}} \cdot 0.3 6^{\frac{1}{3}})

ln (3 x) - 2 ln (x)

ln (a) + ln (\frac{1}{2 b}) - b (\frac{1}{2 b})^{2}

What is simplify-log_{10}(7.5*10^{-3})+log_{10}(3) ?
The solution to simplify-log_{10}(7.5*10^{-3})+log_{10}(3) is 2log_{10}(20)