Log Question?

Question

I don’t remember, but in base 10 can you take a log of an natural number greater than 10? Since log 10 would give you 1. Let’s say log 319? Is that possible or is that mathematically incorrect? It has been a long time since I have dealt with them and don’t remember. Also, when I see log(b)N (where b is a subscript), in base 10, if I write log of 319 is the b this case 10? So it would look something like log(10)319 (where 10 is a subscript again). Thanks!

Answer 1

The log of a number to a given base is the power to which base must be raised to give the number.
Example 1
10² = 100
log(base10) 100 = 2

Example 2
2³ = 8
log(base 2) 8 = 3

Your question refers to the number log(base 10) 319
This is 2.507
ie log(base 10) 319 = 2.507
ie 10^(2.507) = 319

Answer 2

A log can have any value. In log tables they are usually fractions and you have to adjust them.
A log is just the power of a base that will equal a number. A base can be anything but for all practical purposes either e or 10 is used.

The log(10) of 319 is what the value of x is in 10^x=319.
The log(2) of 310 is what the value of x is in 2^x=319.

Answer 3

As long as you're not taking the log of 0 or a negative number, it is valid. log(319) is valid; in fact, floor(log(319)) + 1 will give you the number of digits of 319.

Answer 4

Yes and yes

log 319 = log (10) 319 = 2.50379068 (approx)

Check 10^2.50379068 = 318.999998