SOLUTION: How do you solve problems like 27^(2-x)=(1/3)?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do you solve problems like 27^(2-x)=(1/3)?      Log On


   

Question 543180: How do you solve problems like 27^(2-x)=(1/3)?
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
27%5E%282-x%29=%281%2F3%29
To solve this, you can use the ln(x) function. We know that:
ln%28a%5En%29=n%2Aln%28a%29
What that means is, if you apply the natural log function to both sides of the equation - you can just bring the exponent down in front like so:
ln%2827%5E%282-x%29%29=%282-x%29ln%2827%29
Which makes your problem much easier to work with.
27%5E%282-x%29=%281%2F3%29=3%5E-1 becomes
%282-x%29ln%2827%29=%28-1%29%2Aln%283%29
How to solve:
%282-x%29ln%2827%29=-ln%283%29

2-x=-1%2F3
-x=-1%2F3-2
x=1%2F3%2B2
x=7%2F3