my question is below...

Question

How do I express 10^5 as a power of 3?

Also, please explain and/or show work, I want to able to do this by myself next time! :)

Answer 1

Set 10⁵ equal to 3^x and solve for x.

 

3^x = 10⁵

 

log(3^x) = log(10⁵)

 

x log3 = 5

 

x = 5 / log3

 

Then 3 to the power 5/log3 gives 10⁵.

 

3^5/log3 = 10⁵