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Math Help - Equation rearrangment

  1. #1
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    Equation rearrangment

    How do I rearrange 3^(x+2) - 3^x = 1000000 to work out x. New to the forum so not sure how to type it but question is 3 to the power of (x+2) minus 3 to the power of x. I have even worked out an answer by trial and error of 10.682630385 but can't for the life of me see how to rearrange the equation (guessing there will be a log base 3 in there somewhere). Thanks David
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  2. #2
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    Quote Originally Posted by aitchd View Post
    How do I rearrange 3^(x+2) - 3^x = 1000000 to work out x. New to the forum so not sure how to type it but question is 3 to the power of (x+2) minus 3 to the power of x. I have even worked out an answer by trial and error of 10.682630385 but can't for the life of me see how to rearrange the equation (guessing there will be a log base 3 in there somewhere). Thanks David
    take out in the LHS. it gives. .
    can you do it now??
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  3. #3
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    I dont see the symbols in the answer just a lot of dots and dashes between take and out and after gives. Do I have a font that I need missing. I am on my work computer so not sure what changes I can make to the setup.
    David
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  4. #4
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by aitchd View Post
    I dont see the symbols in the answer just a lot of dots and dashes between take and out and after gives. Do I have a font that I need missing. I am on my work computer so not sure what changes I can make to the setup.
    David
    okay tell me if this is visible.
    take 3^x out in the LHS to get (3^x)(9-1)=1000000. so 3^x=(1000000/8).
    now can you see where the log to the base three comes in?
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  5. #5
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    O.K I have gone on to another computer and can see your answer now although I still don't know what to do to get the other one to work or how to use the symbols at the bottom of the post window. Unfortunately I still don't get the answer and also cant get my head around what you have done to get 3 to the power of x times 0.8 = 1000000. If I have read this right I would rearrange to 3 to the power of x = 1000000 divided by 0.8 = 1250000. Interstingly this is the total of the two answers I get. Then I would do log base 3 of 1250000 and get an answer of 12.7785 which I dont believe is correct. Have I read your answer wrong and does it mean 3 to the power of (x times 0.8) Thanks for your help
    David
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  6. #6
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    Sorry we are both writing posts at the same time. What you have written is visable to me and now that I see 8 and not 0.8 I do indeed get the right answer thanks. The bit I am still unsure of is the original bit of taking the 3^x out. where does the 9-1 come from. David
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  7. #7
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    Quote Originally Posted by aitchd View Post
    O.K I have gone on to another computer and can see your answer now although I still don't know what to do to get the other one to work or how to use the symbols at the bottom of the post window. Unfortunately I still don't get the answer and also cant get my head around what you have done to get 3 to the power of x times 0.8 = 1000000. If I have read this right I would rearrange to 3 to the power of x = 1000000 divided by 0.8 = 1250000. Interstingly this is the total of the two answers I get. Then I would do log base 3 of 1250000 and get an answer of 12.7785 which I dont believe is correct. Have I read your answer wrong and does it mean 3 to the power of (x times 0.8) Thanks for your help
    David
    What he has done is to take 3^x common.

    3^(x+2) = 3^x multiplied by 3^2 => (hence you add the powers to get x + 2)

    Therefore, it becomes (3^x)(3^2 - 1) = 1000000
    Therefore, (3^x) * 8 = 1000000
    Therefore, 3^x = 125000

    and then you can easily use log to calculate x.

    Is this clear?
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  8. #8
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    Yes it all makes sense now thanks although I would never have got it left to my own devices. Thank you both for all your help. David
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