SOLUTION: If (3^5x)(27^5x)=(3^48)(9^9x), then what is the value of x? I tried to solve for x as a regular equation and got stuck when x was isolated on one side as an exponent.....(3^5x)(

Algebra ->  Exponents -> SOLUTION: If (3^5x)(27^5x)=(3^48)(9^9x), then what is the value of x? I tried to solve for x as a regular equation and got stuck when x was isolated on one side as an exponent.....(3^5x)(      Log On


   

Question 629636: If (3^5x)(27^5x)=(3^48)(9^9x), then what is the value of x?
I tried to solve for x as a regular equation and got stuck when x was isolated on one side as an exponent.....(3^5x)(27^5x)=(3^48)(9^8x)
81^10x=(3^48)(9^8x)
9^2x=(3^48)
Also tried....
10x=48+8x
2x=48
x=24
the answer is 12

Thank you
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
(3^5x)(27^5x)=(3^48)(9^8x)

(3^5x)((3^3)^5x)=(3^48)((3^2)^8x)

(3^5x)(3^(15x))=(3^48)(3^(16x))

3^(5x+15x) = 3^(48+16x)

3^(20x) = 3^(48+16x)

Since the bases are equal, the exponents are equal. So

20x = 48+16x

20x - 16x = 48

4x = 48

x = 48/4

x = 12

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