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bizzeizzy

  • one year ago

Solve the exponential equation. 8^3x =32

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  1. butterflydreamer
    • one year ago
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    |dw:1433325126056:dw|

  2. bizzeizzy
    • one year ago
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  3. butterflydreamer
    • one year ago
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    here are some hints :) |dw:1433325279296:dw|

  4. butterflydreamer
    • one year ago
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    firstly simplify |dw:1433325406385:dw|

  5. bizzeizzy
    • one year ago
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    512?

  6. butterflydreamer
    • one year ago
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    3 times 3x does not equal to 512.. 3 * 3x = 3 * 3 * x = ? So what does 3 times 3 equal to?

  7. bizzeizzy
    • one year ago
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    oh sorry lol.. 9

  8. bizzeizzy
    • one year ago
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    i put the equation you drew into my calculator and it said 512 haha

  9. butterflydreamer
    • one year ago
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    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
    • one year ago
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    *therefore divide both sides by 9 to find x.

  11. bizzeizzy
    • one year ago
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    okay so the answer is \[\frac{ 5 }{ 9 }\] !

  12. butterflydreamer
    • one year ago
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    that's corrreect :)

  13. anonymous
    • one year ago
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    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
    • one year ago
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    haha that's also true :) Nice job!

  15. anonymous
    • one year ago
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    yeah haha XD No problem, its lovely how Mathematics can be solved with different methods.

  16. bizzeizzy
    • one year ago
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    thank you both!

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