Question 1141279: LN (T2) = 2.2846
T2 =???
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! ln(x) = y if and only if e^y = x.
ln(T2) = 2.2846 if and only if e^2.2846 = T2.
solve for T2 to get T2 = 9.821756735.
confirm by replacing T2 with 9.821756735 in ln(T2) = 2.2846 to get ln(9.821756735) = 2.2846 becomes 2.2846 = 2.2846 which is true.
if you meant T^2 (T squared), rather than T2, then you would do the following.
ln(T^2) = 2.2846 becomes 2 * ln(T) = 2.2846
solve for ln(T) to get ln(T) = 2.2846 / 2 = 1.1423.
ln(T) = 1.1423 if and only if e^1.1423 = T.
solve for T to get T = 3.133968209.
confirm by replacing T with 3.133968209 in ln(T^2) = 2.2846 to get ln(3.133968209^2) = 2.2846 which becomes 2.2846 = 2.2846.
the basic logarithm rules for the base of e are:
ln(x) = y if and only if e^y = x.
e is the scientific constant of 2.718281828.....
ln(x^a) = a * ln(x)
ln(e) = 1
you can use the natural log function of your calculator.
pretty much all scientific calculators have them.
if you don't have a scientific calculator, you can use the only one at https://www.eeweb.com/tools/calculator
on most scientific calculators, log function is log to the base of 10 and ln function is log to the base of e.
you should read the instructions to see how to use any of these calculators.
they each have their own unique way of doing things.
the one that i use a lot can be found at http://www.alcula.com/calculators/scientific-calculator/
it's a very nice calculator but does require the flash player to be used.
once you get hang of using it, it's very useful.
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