Question 241969: e^x=10 Help I am so lost.. what would the approximate value be for x?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! e^x = 10
this is an exponential problem.
you need logarithms to solve it.
you can use the log function of your calculator or you can use the ln function of your calculator.
the base e is the scientific constant of 2.718281828.....
This is an irrational number which means it is not the result of a division of two integers.
the fractional part is endless and non repeating.
the ln function of your calculator is the natural log function which is the inverse of the exponential function using the base of e.
exponential functions have the unknown value as the exponent.
10^x is an exponential function
2^x is an exponential function
3^x is an exponential function
e^x is an exponential function
if the problem was 10^x = 10, you could probably solve this easily enough since 10^1 = 10
you would then say x = 1 and the problem would be solved.
if the problem was 10^x = 100, you could probably solve this easily enough since 10^2 = 10*10 = 100
if the problem was 10^x = 50, you might have a little more difficulty solving this.
that's where logs come in.
by definition, 10^2 = 100 if and only if log(100) = 2
they are inverse processes. you use exponents to get there and you use logarithms to get back.
if the question was:
10^x = 100
you could solve it by logarithms.
you would take log of both sides of the equation to get:
log(10^x) = log(100)
by the laws of logarithms, log(10^x) = x * log(10)
you do need to know the laws of logarithms to help you solve these types of problems.
your equation of log(10^x) = log(100) becomes:
x*log(10) = log(100)
you divide both sides of this equation by log(10) to get:
x = log(100)/log(10) and you get:
x = 2 after you find the log of 100 and the log of 10 in your calculator.
you confirm your answer is correct by taking your original equation of:
10^x = 100
and replacing x with 2 to get:
10^2 = 100
which is correct so you solved the problem correctly.
your original problem is:
e^x = 10
you would solve this the same way.
take the log of both sides of the equation to get:
log(e^x) = log(10)
use the laws of logarithms to get:
x * log(e) = log(10)
divide both sides of this eqution by log(e) to get:
x = log(10)/log(e)
use your calculator to find log(10) and log(e) and solve for x to get:
x = 2.302585093
replace x with that in your original equation of:
e^x = 10 to get:
e^(2.302585093) = 10 which becomes:
10 = 10 confirming your answer is correct.
if you can't get e on your calculator, then use the approximation of 2.718281828 for it.
you'll get close but not right on.
2.718281828^(2.302585093) = 9.99999999996 which is very close but not right on.
if you want to find the value of e on your calculator, you need to follow the instructions of your calculator.
my calculator is a TI-30XA (maybe $12.00 or so).
to display the value of e i would do the following:
enter 1
enter 2d ln
that displays e^1 which is the value of e
if i want to store that, i enter:
sto 1
the value of e is stored in memory location number 1
i can then use the value of e not rounded whenever i need it.
you need to review basic exponents and basic logarithms if you're having great difficulty with this.
try this website.
Purple Math
try this one also.
WTAMU
try some lessons from Algebra.Com Lessons
Search for the ones you need.
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