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,

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)   (Show Source): You can put this solution on YOUR website!

=
81 = 9^2
=
=
-------------------------------
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)   (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

Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
solve for x:
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

:

;

Convert 81 to 9^2

Using the exponents of like terms we can get rid of the denominator and have

We can factor out the exponent on the right to

That looks familiar doesn't it, therefore
x = 3

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