Question

Use a calculator to find a number "a" for which e^x>x^5 for all x>a

Answer 1

\[e^x>x^5 for~all~x>a\]

Answer 2

@.Sam. Do you know how to do this?

Answer 3

\[e ^{x}>x ^{5}\]
\[\ln(e ^{x})>\ln(x ^{5})\]
\[x>5\ln(x)\]
\[\frac{x}{lnx}>5\]

Answer 4

Use calculator solve for x

Answer 5

then the values of x is a
a>0

Answer 6

Ok, now how do you use the calculator in find the values of x in the first place?

Answer 7

\[\frac{x}{lnx}>5\]
\[\frac{x}{lnx}-5>0\]
\[\frac{x-5\ln(x)}{\ln(x)}>0\]
Form here, x must be >1
because if x=1, ln(1) from the denominator will be =0 which leads to infinity,
x cannot be negative number because ln(-anything) is infinity, so, x>1 is the answer

Answer 8

Thank you!