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
Simple statements like that are often just the first step in a generalized description: enough to give you an idea of a concept, but might not tell the whole story.
In this case, think of how exponents work. 2·2 = 2^(2) = 4. 2·2·2 = 2^(3) = 8. 2^(5) = 2·2·2·2·2 = 32, which is also 4·8 = 2^(2)·2^(3). Something like this works for every base number and any exponent, so we can generalize that to x^(a)·x^(b) = x^(a+b): to multiply powers of the same base, you can just add their exponents together.
Now look at roots. By definition, √x · √x = x. If we write that as exponentials, we get (√x)^(2) = x^(1). It makes sense then to consider a square root the halfth power since 2·½ = 1: √x = x^(½) = x^(0.5). Higher-power roots are then just fractional exponents.
And now back to logarithms. 0.778 is the same as 778/1000, so 10^(0.778) = 10^(778/1000) = ^(1000)√(10^(788)). You probably don’t want to calculate the exact value that way, but that’s what it means.
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