SOLUTION: solve for x: (9a^2b)^x(3ab)^4=9^5a^10b^7 I am not sure how to solve for x or even how to isolate it when it is an exponent. Especially when there are so many other variables(a,

Algebra ->  Square-cubic-other-roots -> SOLUTION: solve for x: (9a^2b)^x(3ab)^4=9^5a^10b^7 I am not sure how to solve for x or even how to isolate it when it is an exponent. Especially when there are so many other variables(a,       Log On


   

Question 475131: solve for x: (9a^2b)^x(3ab)^4=9^5a^10b^7
I am not sure how to solve for x or even how to isolate it when it is an exponent. Especially when there are so many other variables(a, b) and a huge number (9 raised to the 5th power=59,049). There is just too much going on with this one for me to solve on my own.
Thank you in advance!
Jessica Ortiz
Found 3 solutions by Alan3354, solver91311, ankor@dixie-net.com:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%289a%5E2b%29%5Ex%2A%283ab%29%5E4=9%5E5a%5E10b%5E7
= %289a%5E2b%29%5Ex+=+9%5E5a%5E10b%5E7%2F%2881a%5E4b%5E4%29
81 = 9^2
= %289a%5E2b%29%5Ex+=+9%5E3a%5E10b%5E7%2F%28a%5E4b%5E4%29
= %289a%5E2b%29%5Ex+=+9%5E3a%5E6b%5E3
-------------------------------
I shoulda spotted that the RHS is the cube of the LHS.
ankor... did.
I'll blame it on drugs (headache meds).

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Break everything in the LHS into pieces:



First thing to note is that

Next, substitute and rearrange:



Use the sum of exponents rule:



Now this uglier-than-a-mud-fence expression is equivalent to the original Left Hand Side, which we were told was equal to the original right hand side, hence:



Now all we need to do is find a value for such that , and , and

Can you take it from here?

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve for x: %28%289a%5E2b%29%5Ex%29%283ab%29%5E4=9%5E5a%5E10b%5E7
yes, it looks pretty hairy, but let's just plunge into it and see how much we can simplify it
:
We will leave expression with the x exponent alone for while
%28%289a%5E2b%29%5Ex%29%283%5E4a%5E4b%5E4%29=9%5E5a%5E10b%5E7
:
%28%289a%5E2b%29%5Ex%29%2881a%5E4b%5E4%29=9%5E5a%5E10b%5E7
;
%289a%5E2b%29%5Ex=%289%5E5a%5E10b%5E7%29%2F%2881a%5E4b%5E4%29
Convert 81 to 9^2
%289a%5E2b%29%5Ex=%289%5E5a%5E10b%5E7%29%2F%289%5E2a%5E4b%5E4%29
Using the exponents of like terms we can get rid of the denominator and have
%289a%5E2b%29%5Ex=%289%5E3a%5E6b%5E3%29
We can factor out the exponent on the right to
%289a%5E2b%29%5Ex=%289a%5E2b%29%5E3
That looks familiar doesn't it, therefore
x = 3