Jadedry one year ago Solve the following equation:

$3^{2x+1} -26(3^x) - 9 = 0$ I have no idea where to start, could you please provide some hints? Thanks in advance!

2. anonymous

do u want answer in terms of x or want to simplify it?

3. ganeshie8

Let $$3^x = t$$

4. anonymous

as ganeshie said but before line up the variables so everything clear like this

5. anonymous

$-9-26 \times 3^{x}+3^{2x+1}=0$

6. anonymous

$-9-26 \times 3^{x}+3(3^{x})^{2}$

7. anonymous

$3t ^{2}-26t-9=0$

8. anonymous

then factorise it

@ayeshaafzal221 I believe I'm supposed to solve for X, I got the same equation you did, but my textbook says that the answer is 2?

10. anonymous

11. anonymous

This is why math makes no sense... I read the equation, i caught on for the next part, then all that sht fell apart in my head

12. anonymous

$(t-9)(3t+1)=0$

13. anonymous

split this into two eq

14. anonymous

$t-9=0 , 3y+1=0$

15. anonymous

now from t-9=0 -> t=9

16. anonymous

sub back the t value

17. anonymous

$3^{x}=9$

18. anonymous

English plz xD (I dont needa know this stuff I'm just looking at wat u guys r doing)

19. anonymous

$3^{2}=9$

20. anonymous

$3^{x}=3^{2}$

21. anonymous

and for the other eq 3y-1=0 -> y=-1/3 has no solution

22. anonymous

so x=2

ah yes of course, I'm so stupid. X.X - I forgot to convert the "t" back to the 3x^2

24. anonymous

thats ok hope it helps :)

Thank's ayeshaa, I had some other problems with the same line of thought, I'll be able to solve them now. ;u;