Solve the following indicial equation?

Question

#25^(2-x)=1/5#

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Answer 1 · 2017-07-23T23:27:39

#x = frac(5)(2)#

We have: #25^(2 - x) = frac(1)(5)#

Let's express all numbers in terms of #5#:

#Rightarrow (5^(2))^(2 - x) = 5^(- 1)#

Using the laws of exponents:

#Rightarrow 5^(4 - 2 x) = 5^(- 1)#

#Rightarrow 4 - 2 x = - 1#

#Rightarrow - 2 x = - 5#

#therefore x = frac(5)(2)#

Therefore, the solution to the equation is #x = frac(5)(2)#.