one more question

[Guest]

Can you help me solve for m? I forgot how to solve this in a simple way :?

(1/5)^m(1/4)^18=1/210^55

 

[tkhunny]

One More Question

I think no one will hold you to that.

I see no "simple" way to proceed. I guess there is one thing you could do, but I wouldn't call it simple.

(1/4)^18 = ((1/2)^2)^18 = (1/2)^36
(1/210)^55 = (1/(2*105))^55 = (1/2)^55 * (1/105)^55

Then

(1/5)^m * (1/4)^18 = (1/210)^55

changes to

(1/5)^m * (1/2)^36 = (1/2)^55 * (1/105)^55

Which can be simplifed a bit

(1/5)^m = (1/2)^19 * (1/105)^55

After that, I'm tempted to break out the logarithms.

 

[Guest]

tkhunny, thank you so much for your help. I think that's as far as I want to go with this problem, since it makes enough sense to me this way. No logs for this one