Calculus
posted by Jon .
In increasing order, rank:
3^ln 2, 2^3, 2^ln 3
*do not use a calculator, and explain your choices
Obviously, 2^3=8
So, instinctively, I entered the other values into my calculator just to rank the quantities using decimal places. However, in my calculator, 3^ln 2 and 2^ln 3 both yield: 2.1414886064.
So, can someone explain this problem to me please!

2^3
take ln and get ln(2^3) = 3 ln 2
3^ln 2
take ln and get ln (3^ln 2) = ln 2 ln 3
2^ln 3 also gives ln 3 ln2
and ln 3 <3
Respond to this Question
Similar Questions

math
belinda used her calculator to find the decimal for the fraction 21/28. When she entered 21/28, the calculator gave her an answer that looked familiar. Why do you think she recognized it? 
math
belinda used her calculator to find the decimal for the fraction 21/28.When she entered 21/28, the calculator gave an answer that looked familiar. Why do you think she recognized it? 
math
x^3 + 4x^2 + 14x + 20 use the root or zero feature of a graphing utility to approximate the zeros of the function accurate to three decimal places. I do not know how to use the root or zero feature on my calculator. If someone could … 
Chemistry
Can someone please help me with these chemistry questions...I just don't get it! 1. Using the following elements, rank them in order of increasing melting points, based on the periodic trend for melting point: Sr, Mg, Be, Ba? 
Math
Can someone please help me with these three question? 
Chemistry
Rank the following solutions in order of increasing acidity. 1 M phenol 1 M boric acid 1 M cyanic acid 1 M formic acid 1 M hydrochloric acid 2. Rank the following solutions in order of increasing basicity. 1 M C3H5O3Na 1 M KF 1 M KOCN … 
Chemistry
(a)What is the bond order of the diatomic molecule BN? 
Chemisty !!
(a) Why do the densities of most liquids increase as they are cooled and solidified? 
Mathematics concepts
Matthew sits at his desk unable to figure out the answer to a division problem. He reaches into his desk and pulls out a calculator. What is the correct response for Matthew's teacher to have? 
Math
Belinda used her calculator to find the decimal for the fraction 21/28, When she entered 21/28 the calculator gave an answer that looked familiar. Why do you think she recognized it.