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
Well, I want to try to help you tackle this is two ways.
First, you have to know that the nth root of x^m is x^(m/n). Now, since 0.778 = 778/1000, then 10^0.778 = 10^(778/1000) = the 1000th root of 10^788.
These are properties of exponents that should should get very used to:
x^(m) * x^(n) = x^(m+n)
x^(m) / x^(n) = x^(m-n)
(x^(m))^(n) = x^(m*n)
(x*y)^(m) = x^(m)*y^(m)
x^(-n) = 1 / x^(n)
x^(0) = 1
Once you have those firmly understood, then helping you understand what a logarithm is is much simpler. Let’s try. Follow along and answer these if you can at home. (You’ll learn it much faster than if you’re given the answer.)
What power do you raise 3 to in order to get 27? [Hint: I am asking you for y in: 3^(y)=27]
What power do you raise 4 to in order to get 16?
What power do you raise 5 to in order to get 625?
… [This question is such an easy one to ask that it gets asked a lot. Let’s try to generalize it.]
What power do you raise **b** to in order to get **x**?
If you answered the first three, then you were already doing logarithms. Logarithms are asking you what power of **your base** you have to raise it to get **a specific number, x.** [In an equation b^(y)=x]
Hence was born log_b(x). Everyone happens to use a base 10 number system, so oftentimes when you see log(x) it is implied that b = 10. There are some scenarios where it is assumed that b = e = 2.7182818284590452…, but it general that is referred to as ln(x).
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