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What is Common ?

  1. Dec 7, 2004 #1
    Find the exact value of x: 25^x-30(5^x)+125=0 what is the common base? I thought it was 5 but not for 30.
  2. jcsd
  3. Dec 7, 2004 #2
    Have a look at the form of the equation... can you do a subsitution?
  4. Dec 7, 2004 #3


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    HINT: Observe that [itex]25 = 5^2[/itex]
  5. Dec 7, 2004 #4
    Also, simplify the equation first.
  6. Dec 7, 2004 #5
    First of all can the -30(5^x) be multiplied? to =-150^x
    Next I let A=5^x and then my equation became A^2-30+125=0 so A^2+95 I dont think I did this right and if I did then what do I do next A=square root of -95?
  7. Dec 7, 2004 #6
    Nope. Observe that 2*3^4 = 2*(3^4) = 2*3*3*3*3. On the other hand, (2*3)^4 = 2*2*2*2*3*3*3*3 which is definitely not equivalent.
    Note that your equation can be written (5^x)^2 - 30(5^x) + 125 = 0, so if A = 5^x, the equation becomes A^2 - 30A + 125 = 0.
  8. Dec 7, 2004 #7
    Ok I factored that and got (A-5) (A-25) A=5 or A=25 sooo 5^x=5 or 5^x=25
    x=1 or x=2 are my solutions correct? Can there be two values for x?
  9. Dec 7, 2004 #8
    Plug the values of x you solved for back into the original equation to see if they work. :smile:
  10. Dec 8, 2004 #9
    Yeah! This is the best method to vertify the answer.
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