How to Solve for 'x' When It's an Exponent?

Question

Basically, I have this equation...

 

60 = 400(0.85)^x

 

...And I need to solve for 'x'.

So far, what I'm thinking is that I need to divide both sides by 400, but I haven't got past that yet because I'm stuck.

 

60 = 400(0.85)^x   -->   0.15 = (0.85)^x

 

I'm confused because, since 'x' is being used as an exponent, I don't know how to continue. I don't think I would do the square root (not really square root, more like... I don't know... "x root"?) of it though because wouldn't that cancel it out?

Help? >.<

Answer 1

You did great for the first step. Next you would want to use logarithms to solve.

 

So, here's the next step:

 

log.15=log.85^x (remember that when there is an exponent in a logarithm, it is moved in front of the log as a multiplier)

 

log(.15)= x log(.85)

 

x= log(.15)/log(.85)

 

x=11.6732

 

And now plug the number in for x to check if the solution is correct. It comes out to about the same, just since it is rounded slightly.

 

Whenever you are trying to solve for x or another variable (where it is in the exponent) in a situation like this, you want to use logarithms to solve for it.