Please help people... Simplify 5^2x - 24 * 5^x = 25

Question

anonymous · Answer

i assume "simplify" actually means "solve for $x$ in this case, right?

anonymous · Answer

yessh :)

anonymous · Answer

start with 
$$5^{2x}-24\times 5^x-25=0$$ factor as 
$$(5^x-25)(5^x+1)=0$$

anonymous · Answer

if that is confusing, note that $5^{2x}=(5^x)^2$ and think of it as 
$$u^2-24u-25=0$$ where $u=5^x$ then it will be easier to see how to factor it

anonymous · Answer

uhh yah but cudnt yer just multiply the 5^2x and da 5^x and get 5^3x?

anonymous · Answer

once you have it factored as 
$$u^2-24y=u-25=(u-25)(u+1)$$ then replace $u$ by $5^x$ to get 
$$(5^x-25)(5^x+1)=0$$ and solve for $x$
notice that $5^x+1=0$ has not solutions, because $5^x>0$ always

anonymous · Answer

it is not a multiplication, so no you cannot

anonymous · Answer

but they arent any brackets, so?

anonymous · Answer

coz im guessin if they wer brackets like (5^2x -24) * 5^x then u cudnt multiply..