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Power. It is the number of times you use the base as a factor in a multiplication problem.
The main use for a logarithm is to find an exponent. If N = a^x Then if we are told to find that exponent of the base (b) that will equal that value of N then the notation is: log N ....b And the result is x = log N ..........b Such that b^x = N N is often just called the "Number", but it is the actuall value of the indicated power. b is the base (of the indicated power), and x is the exponent (of the indicated power). We see that the main use of a logarithm function is to find an exponent. The main use for the antilog function is to find the value of N given the base (b) and the exponent (x)
"It is easy to use an exponent in a sentence." There, that sentence uses it!
A rational exponent means that you use a fraction as an exponent, for example, 10 to the power 1/3. These exponents are interpreted as follows, for example:10 to the power 1/3 = 3rd root of 1010 to the power 2/3 = (3rd root of 10) squared, or equivalently, 3rd root of (10 squared)
Oh, dude, factoring with an exponent to the power of 4 is like breaking up with your high school sweetheart - it's complicated but doable. You basically look for common factors and use the power rule to simplify it. So, you're just dividing the exponent by 4 and seeing what's left. Easy peasy, lemon squeezy!