SOLUTION: A googl is 10 to the 100th power (which is 1 followed by 100 zeros). So, if googl =(x^5)^10 then what is the value of x? There are two solutions to this. I only have one.Please he

Algebra ->  Equations -> SOLUTION: A googl is 10 to the 100th power (which is 1 followed by 100 zeros). So, if googl =(x^5)^10 then what is the value of x? There are two solutions to this. I only have one.Please he      Log On


   

Question 98535: A googl is 10 to the 100th power (which is 1 followed by 100 zeros). So, if googl =(x^5)^10 then what is the value of x?
There are two solutions to this. I only have one.Please help me find the second one! THANKS IN ADVANCE!
(x^5)^10 = x^50
x^50 = 10^100
x = 10^2
x = 100

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%5E5%29%5E10=10%5E100 Start with the given equation

x%5E50+=+10%5E100 Distribute and multiply the exponents.


root%2850%2Cx%5E50%29+=+root%2850%2C10%5E100%29 Take the 50th root (it's like the square root) of both sides


x+=+root%2850%2C10%5E100%29 The left side is now x

x+=+%2810%5E100%29%5E%281%2F50%29 Rewrite root%2850%2C10%5E100%29 as %2810%5E100%29%5E%281%2F50%29


Distribute and multiply the exponents. Remember, when taking the even root (such as a square root) there is a positive and negative answer
x+=+%2810%29%5E%28100%2F50%29 or x+=+-%2810%29%5E%28100%2F50%29


x+=+10%5E2 or x+=+-10%5E2 Reduce


x+=+100 or x=-100 Square 10 to get 100

So the answers are x+=+100 or x=-100