MATHS help (LOGS)?

Question

How does log 1.10 = 0.0953?
why does log (e^x) = x?

Answer 1

log 1.1 = .0953 ==> we're dealing with natural logs, i.e., base e. So anotehr way of looking at the question is e^x = 1.1, and e^.0953 = 1.1

Similarly, in the second eq'n, let z be the unknown. Then e^z = e^x, and z = x

Answer 2

There's two types of logs - logs to base 10 and natural logs.

If you do 'ln 1.10' on your calculator you'll get 0.0953 whilst log 1.10 will give you 0.041

ln and exp are inverts, just like if you multiply 3 by 5 and divide by 5 you get 3 if you take the exp of 3 and then take log of 3 you'll get 3.

Jus remember its ln x and exp x that are inverts and log x and 10^x

Answer 3

ln 1.10 = 0.09531 because e^0.09531 = 1.1

ln(e^x) = x because the log(subscript)n of n^x is defined to be x

Answer 4

For log (e^x) = x remeber that

log (a^b) = b * log(a)

so log(e^x) = x * log(e)

Now, as long as you are using NATURAL log's (normally written ln(x) ) log(e) = 1 by definition.