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coolaidd

  • 3 years ago

solve. then round answer to the nearest hundredth. 6^x-3=52

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  1. coolaidd
    • 3 years ago
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    |dw:1342135467157:dw|

  2. dpflan
    • 3 years ago
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    \[6^{x-3} = 52\]You will need to use logarithms to solve this one

  3. dpflan
    • 3 years ago
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    Specifically, you will need to use the property of logarithms such that will allow you to work with the exponent: So, if you have \[x^y\], if you take the log of this you obtain: \[log_a(x^y) = y * log_a(x)\]The exponent now becomes a factor in the product

  4. dpflan
    • 3 years ago
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    For your equation, you will want to take the logarithm of both sides, then you can solve for x. You can use any base for the logarithm: \[log_a\] I'm sure you're familiar with the concept of logarithms, but here is nice way to remember what it does: you can say that when you have the expression: \[log_ab = x\]You are looking for the number you raise 'a' to in order to obtain 'b' is 'x'. \[a^x = b\] \[log_28=3\]The number you raise 2 to in order to obtain the value 8, is 3. \[2^3 = 8\]

  5. dpflan
    • 3 years ago
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    Does this seem familiar or helpful?

  6. coolaidd
    • 3 years ago
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    yes..

  7. dpflan
    • 3 years ago
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    OK, cool, I see that you had a similar question - http://openstudy.com/users/coolaidd#/updates/4fff44afe4b09082c0707aad

  8. coolaidd
    • 3 years ago
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    thanks

  9. dpflan
    • 3 years ago
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    Do you think you can solve this problem?

  10. coolaidd
    • 3 years ago
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    log_5 x=3 x = 5^3 = 125

  11. coolaidd
    • 3 years ago
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    sorry!

  12. coolaidd
    • 3 years ago
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    6^(x - 3) = 52 (x - 3) ln 6 = ln 52 x - 3 = ln 52/ln 6 x = 3 + ln 52/ln 6 ≈ 5.20523

  13. dpflan
    • 3 years ago
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    Yeah, nice!

  14. coolaidd
    • 3 years ago
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    thanks! :)

  15. dpflan
    • 3 years ago
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    Sure, good luck with the rest of your studies! Maybe you can help with some questions even ;)

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