## Kuoministers 2 years ago Help me on this question please... I really dont know where to start thanks!!

1. Kuoministers

$\huge3^{x} + 5 \times 3^{x} = 54$

to start, we need to isolate the variables, we start by dividing both sides by 3^x, then subtract 5 from both sides, and then multiply both sides by 3^x $3^x + 5 \times 3^x \div 3^x = 54 \div 3^x$ $3^x + 5 - 5 = 54/3^x$

$3^x \times 3^x = 54/3^x \times 3^x - 5$

$9^x^2 = 54 -5$

$9^x^2 = 51$ so now we find the square root of each side

$\sqrt{9^x^2} = \sqrt{51}$

the square and square root cancel each other out, so it would be $9^x \approx 7$

8. Kuoministers

im not sure but thats not the answer that is in the back of the book :P

divide both sides by 9 $9^x \div 9 = 7 \div 9$ $^x = 7/9$

10. Kuoministers

@artix_17

11. Kuoministers

thats not the answer in the book :P

12. artix_17

13. Kuoministers

2

14. Kuoministers

i think the way he started the question was wrong cause i was told to keep the same base

15. artix_17

Yea, 3^x X 3^x can be written as 3^2x

16. Kuoministers

yea i agree on that

17. Kuoministers

$\huge3^{2x} + 5 = 3^{3} \times 2$ this might help?

18. artix_17

How did you get that?

19. rizwan_uet

|dw:1359366605554:dw|

20. Kuoministers

i broke up 54 into 3^3 times 2 cause i wanted to make the base the same which in this case 3

21. Kuoministers

I GET IT :D

22. rizwan_uet

|dw:1359366719099:dw|

23. Kuoministers

i didnt see you could factorise 3^x out of that equation!! Thanks so much to both of you :)

24. artix_17

You can do the 3^x X 3^x = 3^2x

25. artix_17

can't*

26. Kuoministers

you cant?

27. artix_17

No, because its actually 3^x + ( 5 X 3^x )

28. artix_17

You have to either solve inside the bracket first or factorize

29. Kuoministers

oh thanks @artix_17 for pointing that out!! I wouldn't have noticed :P

30. artix_17

No problem :)