SOLUTION: 36^-3n ------ = 36 Please help with steps. 216^3n

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 36^-3n ------ = 36 Please help with steps. 216^3n      Log On


   

Question 1135936: 36^-3n
------ = 36 Please help with steps.
216^3n
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

36%5E%28-3n%29%2F216%5E%283n%29+=36

%281%2F36%5E3n%29%2F216%5E%283n%29+=36

1%2F%2836%5E3n%2A216%5E%283n%29%29+=36

1%2F7776%5E%283n%29+=36

1%2F36=7776%5E%283n%29

log%281%2F36%29=log%287776%5E%283n%29%29

log%281%2F36%29=3n%2Alog%287776%29

3n=log%281%2F6%5E2%29%2Flog%287776%29

3n=%28log%281%29-2log%286%29%29%2F5log%286%29........log%281%29=0

3n=-2log%286%29%2F5log%286%29...cancel log%286%29

3n=-2%2F5

n=%28-2%2F5%29%2F3

n=-2%2F15

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
36^-3n
------ = 36 Please help with steps.
216^3n
matrix%281%2C3%2C+36%5E%28-+3n%29%2F216%5E%283n%29%2C+%22=%22%2C+36%29

matrix%281%2C3%2C+%286%5E2%29%5E%28-+3n%29%2F%286%5E3%29%5E%283n%29%2C+%22=%22%2C+6%5E2%29

matrix%281%2C3%2C+6%5E%28-+6n%29%2F6%5E%289n%29%2C+%22=%22%2C+6%5E2%29

matrix%281%2C3%2C+6%5E%28-+6n+-+9n%29%2C+%22=%22%2C+6%5E2%29

matrix%281%2C3%2C+6%5E%28-+15n%29%2C+%22=%22%2C+6%5E2%29

- 15n = 2 ----- Bases are equal and so are their exponents

highlight_green%28matrix%281%2C3%2C+n%2C+%22=%22%2C+-+2%2F15%29%29

You DON'T NEED LOGS or any complex calculations....just the laws of exponents! 

Using logs is just a waste of time and effort, unless you're requested to use logs, of course.