Log Question?

Posted by admin
Ella asked:


5^x + 3^2x = 92
You have to use logs to solve it, and the answer in the back of the book is aprox. 1.93
and guys - YOU CANNOT LOG BOTH SIDES
You can only do that if the sides are single terms such as 5^x * 3^2x
I’ve been told that the answer IS 1.93, but not HOW to get it. please don’t say loyg both sides.. its not right. Thanks..

Carol
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    • This entry was posted on Thursday, May 24th, 2007 at 8:42 pm and is filed under siding. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.

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    2 Responses to “Log Question?”

    1. Terry S Says:
      May 28th, 2007 at 1:38 am

      It may not be possible to answer this using traditional forms. Numerical Analysis will lead you to the answer.

      However, here are some observations that can narrow it down.
      if x = 1, then 5^1 + 3^(2*1) = 14

      if x = 2.then 5^2 + 3^(2*2) = 106

      From this it can be seen that 1 < x < 2

      Since x = 2 is closer to 92, next try x = 1.9. This will be too low so next try 1.91, then 1.92, then 1.93, then 1.94 and keep going unitl you find pivot point. You can keep doing this getting it one decimal place more accurate at a time. Two decimals is probably close enough.

    2. simpleguy Says:
      May 30th, 2007 at 4:06 am

      I’ll back Terry up on this one … there is no analytical solution for a problem of the form a^x + b^x = c where a, b and c are all nonzero real numbers so you must resort to a numerical approximation. you can do nothing to solve or simplify this equation using logarithms … you correctly pointed out that it does not have one of the forms which you can simplify using power or logarithm laws

      I second his method of (educated) trail and error to systematically narrow down the possible range of x to find your answer to required accuracy if you have to do this by hand … i.e. with an old fashioned calculator.