Log 6= 0.778 ( base 10),
In other words when we multiply 10 by itself 0.778 times we get 6.
How would I multiply 10 by itself 0.778 times 🤔?
In: Mathematics
What is 10^(1/2)?
For positive integers x, y we have 10^(x) * 10^(y) = 10^(x+y). Example: 10^(3) * 10^(2) = (10*10*10) * (10*10) = 10^(5).
Now suppose we want the same property to hold for real values of x and y too, because that would be nice.
So, if x = 10^(1/2), what must be the value of x?
We have x*x = 10^(1/2) * 10^(1/2) = 10^(2*(1/2)) = 10^(1) = 10. Thus, 10^(1/2) must be the square root of 10.
Similarly, y = 10^(0.778) = 10^(778/1000) is the unique positive real number such that y^(1000) = 10^(778).
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