Comments on: Log Question? http://www.about-siding.com/log-question/128/ Your Questions, Our Answers Mon, 21 May 2012 06:09:59 +0000 http://wordpress.org/?v=2.2.1 By: simpleguy http://www.about-siding.com/log-question/128/#comment-210 simpleguy Wed, 30 May 2007 08:06:01 +0000 http://www.about-siding.com/log-question/128/#comment-210 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. 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.

]]> By: Terry S http://www.about-siding.com/log-question/128/#comment-209 Terry S Mon, 28 May 2007 05:38:51 +0000 http://www.about-siding.com/log-question/128/#comment-209 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. 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.

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