SOLUTION: log base(sq rt of 5) of 25^4x-1= 3 for this problem i realized (sq rt of 5)^3 equals 25^4x-1 that simplifies to 5*(sqrt of 5)= 25^4x-1 now you divide both sides by 5 and

Question 488974: log base(sq rt of 5) of 25^4x-1= 3
for this problem i realized (sq rt of 5)^3 equals 25^4x-1
that simplifies to 5*(sqrt of 5)= 25^4x-1
now you divide both sides by 5 and get (sq rt of 5)=5^4x-1
4x-1=0.5 so 1.5=4x
so x=.375
i spent sooooo long on this problem so i wanted to assure that all my work is correct and i got the problem correct. i want to make sure i got it right! any comfirmation/correction is appreciated! thanks!
Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
You made only one mistake, but of course that is one too many.
5*(sqrt of 5)= 25^4x-1
now you divide both sides by 5 and get (sq rt of 5)=5^4x-1
When you divide 25^y by 5 you do not get 5^y, you get 5^(2y-1) due to 2 rules for computing these exponent operations..
1. 25^y = (5^2)^y = 5^(2y)
2. (5^z)/5 = 5^(z-1).
Now apply this to your given problem and solve for x similar to how you did before. Hint: it's still a fraction, slighly larger.

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