1. ## 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

2. 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 $3^x$ out in the LHS. it gives. $3^x \cdot 8=1000000$.
can you do it now??

3. 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

4. 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?

David

6. 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

7. Originally Posted by aitchd
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?

8. 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