What is log_{10}((1000c^5)/(2d^4)) ?

The solution to log_{10}((1000c^5)/(2d^4)) is 2+log_{10}(5)+5log_{10}(c)-4log_{10}(d)

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simplify log_{10}((1000c^5)/(2d^4))

simplify

lo g_{10} (\frac{1000 c ^{5}}{2 d ^{4}})

2 + lo g_{10} (5) + 5 lo g_{10} (c) - 4 lo g_{10} (d)

Solution steps

lo g_{10} (\frac{1000 c ^{5}}{2 d ^{4}})

Factor the number:

1000 = 2 \cdot 500

= lo g_{10} (\frac{2 \cdot 500 c ^{5}}{2 d ^{4}})

Cancel the common factor:

2

= lo g_{10} (\frac{500 c ^{5}}{d ^{4}})

Apply log rule:

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

lo g_{10} (\frac{500 c ^{5}}{d ^{4}}) = lo g_{10} (500 c^{5}) - lo g_{10} (d^{4})

= lo g_{10} (500 c^{5}) - lo g_{10} (d^{4})

lo g_{10} (500 c^{5}) = 2 + lo g_{10} (5) + 5 lo g_{10} (c)

lo g_{10} (d^{4}) = 4 lo g_{10} (d)

= 2 + lo g_{10} (5) + 5 lo g_{10} (c) - 4 lo g_{10} (d)

lo g_{2} (2000) - lo g_{2} (150)

lo g_{5} (4) + lo g_{5} (6)

lo g_{9} (Y) + 5 lo g_{9} (U) + \frac{2 lo g _{9} ( O )}{3}

lo g_{10} (5 x^{4} y)

ln (\frac{( x + 1 ) ( x - 10 )}{( x - 1 ) ( x + 10 )})

What is log_{10}((1000c^5)/(2d^4)) ?
The solution to log_{10}((1000c^5)/(2d^4)) is 2+log_{10}(5)+5log_{10}(c)-4log_{10}(d)