SOLUTION: hi there I am currently doing exponential equations and indices, which im understanding a few but unable to complete these. Can you assist? 1. 5^2x-6(5^x)+5=0 (5x)^2-6(5^x)+5=0

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Question 662425: hi there I am currently doing exponential equations and indices, which im understanding a few but unable to complete these. Can you assist?
1. 5^2x-6(5^x)+5=0
(5x)^2-6(5^x)+5=0
let 5x=y
y^2-6y+5=0
(this one i have started to work on but unable to finish)
2.4^x(5^2x)=10
3.7^x+1-2=2(7^x)+3
4.6(3^x-1)=3^4-3^x
I would greatly appreciate help thanks.
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi,previously Posted
1. 5^2x-6(5^x)+5=0
(5x)^2-6(5^x)+5=0
let || Good work!
y^2-6y+5=0
factoring
(y-5)(y-1) = 0, y = 5 0r y = 1 AND x = 1 0r x = 1/5
As to the Remainder: the Idea is combining Like Terms...
2.4^x(5^2x)=10 ⇒ , x = 1/2
3.7^x+1-2=2(7^x)+3 ⇒ 7^x(7-2) = 5 ⇒ 7^x = 1, x = 0
4. ⇒
3^x (6*3^(-1)+1) = 3^x(2+1)= 81 ⇒ 3^x = 27, x = 3