## Pinky1234 2 years ago Help Please. 4^2x+3=1

1. Pinky1234

2. jim_thompson5910

is the problem $\Large 4^{2x}+3=1$ OR is it $\Large 4^{2x+3}=1$

3. Pinky1234

yeah that second one

4. jim_thompson5910

Hint: $\Large 4^{2x+3}=1$ $\Large 4^{2x+3}=4^0$

5. Pinky1234

so we are not using that 1?

6. jim_thompson5910

we are, just a different form of it 4^0 is the same as 1

7. Pinky1234

ok

8. jim_thompson5910

the bases are the same (4) so the exponents must be the same

9. jim_thompson5910

so 2x + 3 = 0

10. Pinky1234

yup i Got the answer thanks :)

11. jim_thompson5910

ok great

12. Pinky1234

can you please help me with couple of them too?

13. jim_thompson5910

sure a few more

14. Pinky1234

ok here is another one

15. Pinky1234

$10^{-3x}\times10^{x}=\frac{ 1 }{ 10 }$

16. jim_thompson5910

$10^{-3x}\times10^{x}=\frac{ 1 }{ 10 }$ $10^{-3x}\times10^{x}=10^{-1}$ $10^{-3x+x}=10^{-1}$ I'll let you finish

17. Pinky1234

ok

18. jim_thompson5910

what do you get

19. Pinky1234

$x=\frac{ 1 }{ 2 }$

20. Pinky1234

I need help with couple more pleaseeee!!

21. Pinky1234

$64\times16^{-3x}=16^{3x-2}$

22. jim_thompson5910

-3x + x = -1 -2x = -1 x = 1/2 good

23. Pinky1234

thanks

24. jim_thompson5910

$64\times16^{-3x}=16^{3x-2}$ $(4^3)\times(4^2)^{-3x}=(4^2)^{3x-2}$ $(4^3)\times4^{2(-3x)}=(4)^{2(3x-2)}$ $(4^3)\times4^{-6x}=(4)^{6x-4}$ $4^{3+(-6x)}=(4)^{6x-4}$ $4^{3-6x}=(4)^{6x-4}$

25. Pinky1234

I got an answer: $x=\frac{ 7 }{ 12 }$

26. jim_thompson5910

good

27. Pinky1234

$\frac{ 81^{3n+2} }{ 243^{-n} }=3^{4}$

28. Pinky1234

oh maybe I can do this one let me try first :)

29. jim_thompson5910

alright, tell me what you get

30. Pinky1234

I got $-\frac{ 4 }{ 17 }$

31. jim_thompson5910

you nailed it

32. Pinky1234

:)

33. Pinky1234

$81\times9^{-2b-2}=27$

34. jim_thompson5910

tell me what you get

35. Pinky1234

ok

36. Pinky1234

oh I got that one $-\frac{ 3 }{ 4 }$

37. jim_thompson5910

good, that's correct

38. Pinky1234

ok

39. Pinky1234

$\left(\begin{matrix}1 \\ 6\end{matrix}\right)^{3x+2}\times216^{3x}=\frac{ 1 }{ 216 }$

40. jim_thompson5910

and what did you get

41. Pinky1234

I m having trouble starting it but still trying

42. jim_thompson5910

$\Large \left(\frac{1}{6}\right)^{3x+2}\times216^{3x}=\frac{ 1 }{ 216 }$ $\Large \left(6^{-1}\right)^{3x+2}\times(6^3)^{3x}=6^{-3}$ $\Large \left(6\right)^{-(3x+2)}\times(6)^{9x}=6^{-3}$ $\Large 6^{-(3x+2)+9x}=6^{-3}$

43. Pinky1234

oh I only messed up with one sign