Thread: 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

Originally Posted by aitchd

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??

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

Originally Posted by aitchd

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?

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

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

Originally Posted by aitchd

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?

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