What is log_{10}(40/9)+4log_{10}(5)+2log_{10}(6) ?

The solution to log_{10}(40/9)+4log_{10}(5)+2log_{10}(6) is 5

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simplify log_{10}(40/9)+4log_{10}(5)+2log_{10}(6)

simplify

lo g_{10} (\frac{40}{9}) + 4 lo g_{10} (5) + 2 lo g_{10} (6)

5

Solution steps

lo g_{10} (\frac{40}{9}) + 4 lo g_{10} (5) + 2 lo g_{10} (6)

4 lo g_{10} (5) = lo g_{10} (5^{4})

2 lo g_{10} (6) = lo g_{10} (6^{2})

= lo g_{10} (\frac{40}{9}) + lo g_{10} (5^{4}) + lo g_{10} (6^{2})

Apply log rule:

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

lo g_{10} (\frac{40}{9}) + lo g_{10} (5^{4}) = lo g_{10} (\frac{40}{9} \cdot 5^{4})

= lo g_{10} (\frac{40}{9} \cdot 5^{4}) + lo g_{10} (6^{2})

Apply log rule:

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

lo g_{10} (\frac{40}{9} \cdot 5^{4}) + lo g_{10} (6^{2}) = lo g_{10} (\frac{40}{9} \cdot 5^{4} \cdot 6^{2})

= lo g_{10} (\frac{40}{9} \cdot 5^{4} \cdot 6^{2})

Simplify

\frac{40}{9} \cdot 5^{4} \cdot 6^{2} : 100000

= lo g_{10} (100000)

Factor the number:

100000 = 1 0^{5}

= lo g_{10} (1 0^{5})

Apply log rule:

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

= 5

2 - lo g_{5} (\frac{1}{16}) - \frac{1}{3} lo g_{5} (8)

5 ln (x) + 4 ln (y) - 2 ln (z)

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

4 ln (2) - \frac{1}{2} ln (25)

10 lo g_{10} (\frac{S}{1 0 ^{- 12}})

What is log_{10}(40/9)+4log_{10}(5)+2log_{10}(6) ?
The solution to log_{10}(40/9)+4log_{10}(5)+2log_{10}(6) is 5