## bizzeizzy one year ago Solve the exponential equation. 8^3x =32

1. butterflydreamer

|dw:1433325126056:dw|

2. bizzeizzy

3. butterflydreamer

here are some hints :) |dw:1433325279296:dw|

4. butterflydreamer

firstly simplify |dw:1433325406385:dw|

5. bizzeizzy

512?

6. butterflydreamer

3 times 3x does not equal to 512.. 3 * 3x = 3 * 3 * x = ? So what does 3 times 3 equal to?

7. bizzeizzy

oh sorry lol.. 9

8. bizzeizzy

i put the equation you drew into my calculator and it said 512 haha

9. butterflydreamer

yes so 3* 3x = 3* 3 * x = 9*x = 9x. Therefore we know:|dw:1433326014799:dw| Since the base numbers are the SAME (both are base 2) This means the exponents (power) must be EQUAL.... therefore: |dw:1433326054143:dw|

10. butterflydreamer

*therefore divide both sides by 9 to find x.

11. bizzeizzy

okay so the answer is $\frac{ 5 }{ 9 }$ !

12. butterflydreamer

that's corrreect :)

13. anonymous

I know question is already done. But alternatively you can use the "change of base" method So you have 8 ^ 3x = 32 -> Log both sides ln8^3x = ln32 -> Move the log to the other side, by bring the power down 3x = ln(32) / ln(8) -> Divide the RHS by 3 x = [ln(32)/ln(8)] / 3 = 0.5555556 ~ 5/9

14. butterflydreamer

haha that's also true :) Nice job!

15. anonymous

yeah haha XD No problem, its lovely how Mathematics can be solved with different methods.

16. bizzeizzy

thank you both!