SOLUTION: I am stumped. I know there must be an answer. I studied my exponents like 2^3 = 8 and the inverse of that is 3 = log2(8) and the radical for that is 3 root 8 = 2. But with the s

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Question 635629: I am stumped. I know there must be an answer. I studied my exponents like
2^3 = 8 and the inverse of that is 3 = log2(8) and the radical for that is
3 root 8 = 2. But with the same theory. I was wondering how log 7 = .8451.
10^.8451 = 7.000031591 in the radical form and in the fraction form works as well but I cannot figuire it out in the exponential form. I know there are
formulas and something like b()-1=b(something but can anyone explain how
10^.8451 which is log of 7 is worked out. Do I have to become a master guru just
to get through this.
Answer by jsmallt9(3759) (Show Source):
You can put this solution on YOUR website!
I'm not sure I understand what your question is.

If the question is "How does one find the value of a logarithm?", then there are two main options:
On your own, without help. When finding logarithms on your own they break down into two groups:
Logarithms that can be found with a reasonably small amount of effort. In this category would be logs like or or (1/2), etc. These logs are relatively easy because it is not too difficult to figure out what power of the base results in the argument.
Logarithms which would require a major effort to calculate. In this group would be logs like log(7). It is not easy to find out what power of 10 results in a 7. Since you know that log(7) will be between 0 and 1. After that it get difficult. One way to find log's (or sin's, cos's, etc.) is to use what are called "Taylor's series". (There may be other ways but I cannot think of them at the moment.) Taylor's series use advanced Math (Calculus) to "convert" something like a log (or sin or cos, etc.) into an expression for a decimal approximation that could be calculated by hand. If you want to know more and you know about derivatives then look up "Taylor's series".
With help. Use a calculator or a table of logarithms. This is easy but keep in mind that the calculator will give you decimal approximations most of the time. (This is why is not exactly 7.) And when it does give you an exact answer it may be difficult to tell that it is not an approximation. So I recommend finding logs by hand when possible and using calculators for the rest.