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25^x-1=5^2x-1 -10025^x-1=5^2x-1 -100
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25^x-1=5^2x-1 -100
25^x-1=5^2x-1 -100

User Socialscientist
by
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1 Answer

6 votes

Answer: x=2.

Explanation:


\displaystyle \\25^(x-1)=5^(2x-1)-100\\\\(5^2)^(x-1)=(5^(2x))/(5) -100\\\\5^(2*(x-1))=(5^(2x))/(5) -100\\\\5^(2x-2)=(5^(2x))/(5)-100\\\\(5^(2x))/(5^2) =(5^(2x))/(5) -100\\\\(5^(2x))/(25) =(5^(2x))/(5) -100\ |*25\\\\5^(2x)=5*5^(2x)-2500\\\\5^(2x)+2500=5*5^(2x)-2500+2500\\\\5^(2x)+2500=5*5^(2x)\\\\5^(2x)+2500-5^(2x)=5*5^(2x)-5^(2x)\\\\2500=4*5^(2x)\ |:4\\\\625=5^(2x)\\\\5^4=5^(2x)\ \ \ \ \ \ \Rightarrow\\\\4=2x\ |:2\\\\2=x\\\\Hence\ \ x=2.

User Unbreachable
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