What is log_{10}(4.5x10^{-4}) ?

The solution to log_{10}(4.5x10^{-4}) is log_{10}(45)+log_{10}(x)-5

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simplify log_{10}(4.5x10^{-4})

simplify

lo g_{10} (4.5 x 1 0^{- 4})

lo g_{10} (45) + lo g_{10} (x) - 5

Solution steps

lo g_{10} (4.5 x \cdot 1 0^{- 4})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{10} (4.5 x \cdot 1 0^{- 4}) = lo g_{10} (4.5 x) + lo g_{10} (1 0^{- 4})

= lo g_{10} (4.5 x) + lo g_{10} (1 0^{- 4})

Simplify

lo g_{10} (4.5 x) : lo g_{10} (45 x) - 1

= (lo g_{10} (45 x) - 1) + lo g_{10} (1 0^{- 4})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{10} (1 0^{- 4}) = - 4

= (lo g_{10} (45 x) - 1) - 4

Simplify

(lo g_{10} (45 x) - 1) - 4 : lo g_{10} (45 x) - 5

= lo g_{10} (45 x) - 5

Simplify

lo g_{10} (45 x) : lo g_{10} (45) + lo g_{10} (x)

= lo g_{10} (45) + lo g_{10} (x) - 5

lo g_{2} (9 x) - 4 lo g_{2} (4) - 1

ln ∣ x ∣ + \frac{1}{6 ( \frac{y}{x} ) ^{2}} - ln \frac{y}{x}

\frac{1}{3} ln (x) - ln (x^{2} - 1) + 2 ln (x + 3)

ln (x^{2} - 4) - ln (x - 2)

64 lo g_{4} (3) + 36 lo g_{\frac{1}{6}} (\frac{1}{3})

What is log_{10}(4.5x10^{-4}) ?
The solution to log_{10}(4.5x10^{-4}) is log_{10}(45)+log_{10}(x)-5