How does this work? (Indices)?

I've been given an answer on yahoo answers to the question,


5^6x-1 = 25, but I'm not sure how they got it:





5^6x-1 = 5^2


6x-1 = 2


6x = 3


x = 0.5





How did they get from 5^6x-1 = 5^2 to 6x-1 = 2?


Thanks!How does this work? (Indices)?
log(x^y) base x = y





so log(5^x) base 5 = x.





In most cases, if you do (or undo) any operation on both sides of the equation, nothing really changes.How does this work? (Indices)?
a^m=a^n


implies that m=n


it's a formula


so u already know that 5^2 is 25.therefore,they equated 6x-1 and 2.simple reason!!!
Ask yourself this question,





4^(2) = 4^(x)





What must x be for the equation to hold true?


x = 2 right, because 4^(2) = 4^(2).





Same applies with a slightly more complicated equation.





5^(6x - 1) = 5^2


6x - 1 = 2


x = 1/2





Plug in x = 1/2,


5^(6*(1/2) - 1) = 5^2


5^(3 - 1) = 5^2


5^2 = 5^2 of course.





So generally, it's good to know that


If (m)^x = (m)^y, then x = y.





hope i was of help.
when the bases are the same, then the powers can be compared. that is why you can equate the indices.





so .. if you have something like 3^x = 9, we can say that 3^x=3^2, thus x=2
5^6x-1 = 5^2





a^b=a^c





b log(a)=c log(a)





the log(a) cancels





so b=c





or 6x-1=2

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