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# What is 25 to the power of x equals a fifth

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What is 25 to the power of x equals a fifth

Guest Sep 22, 2017

#1
+76850
+3

Since  25 is a power of 5, the key here is to see if we can equate bases.....

25 = 1/5             note that 25  = 52    and  1/5  =  5-1  .....so we can write

(52)x   =  5-1

52x  = 5 -1         since the bases are the same, we can equate exponents

2x  = -1              divide both sides by 2

x  =  -1/2

CPhill  Sep 22, 2017
edited by CPhill  Sep 22, 2017
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#1
+76850
+3

Since  25 is a power of 5, the key here is to see if we can equate bases.....

25 = 1/5             note that 25  = 52    and  1/5  =  5-1  .....so we can write

(52)x   =  5-1

52x  = 5 -1         since the bases are the same, we can equate exponents

2x  = -1              divide both sides by 2

x  =  -1/2

CPhill  Sep 22, 2017
edited by CPhill  Sep 22, 2017

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