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anonymous

  • one year ago

If I knew all the other values except for n, how would I solve for n in this equation: a_n=a_1 r^((n-1) )

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  1. anonymous
    • one year ago
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    Here is the equation in a better format

  2. anonymous
    • one year ago
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    best way would be to take natural logarithm on both sides

  3. anonymous
    • one year ago
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    and use lograthim properties.

  4. anonymous
    • one year ago
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    is there a simpler way to do it? Because I haven't learned how to do that yet

  5. anonymous
    • one year ago
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    specifically you can use log(ab) = loga + logb property here

  6. anonymous
    • one year ago
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    okat let me think

  7. anonymous
    • one year ago
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    ok thanks

  8. mathstudent55
    • one year ago
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    Usually, when you are solving for an exponent, you need to use logarithms.

  9. A_clan
    • one year ago
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    \[a _{n}/ a _{1} = r ^{n-1}\]

  10. A_clan
    • one year ago
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    Solve LHS. and transform it to a form which is similar to RHS. Then compare

  11. anonymous
    • one year ago
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    Yes I think mathstudent55 is true. But there's one exception, if a_n/a_1 can be written as r^x, then x=n-1. That's the case I can think of solving this without using logarithm.

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