Speaking natural logs, it's '1'.
Speaking common base-10 logs, it can be represented symbolically but not written exactly.
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The value of exponential e is between 2 and 3. The exact number is 2.7182818284.
You can calculate log to any base by using: logb(x) = ln(x) / ln(b) [ln is natural log], so if you have logb(e) = ln(e) / ln(b) = 1 / ln(b)
log base e = ln.
The value of log 500 depends on the base of the logarithm. If the base is 10 (common logarithm), then log 500 is approximately 2.69897. If the base is e (natural logarithm), then log_e 500 is approximately 6.2146. The logarithm function is the inverse of exponentiation, so log 500 represents the power to which the base must be raised to equal 500.
The relationship between e and log is that they are reciprocal of each other.