Tough logarithm problem

Brown said:
I solved the problem by iteration.

Of all the math techniques for solving problems, iteration is about the most unpleasant.
Click to expand...

I used Excel - not a problem.
 
komencanto said:
2^(t/4)-2^(t/5) = 3

How does one figure this out? The answer in my maths books is wrong! I couldn't believe it after spending ages on it, I must have an answer.
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Hmmm. Given the hindsight of the other attempts, let me see if there's another approach.

First, let's go with the suggestion of substitution of x = t/20, so t/4 = 5x and t/5 = 4x.

2^(5x) - 2^(4x) = 3.

Hmm. Let y = 2^x = 2^(t/20).

y^5 - y^4 = 3

Huh. That suggests factoring it as

y^4(y-1) = 3

but I don't see how that helps. Damn.

Does your textbook give an exact answer? Given that, we might be able to backtrack.
 
Brown said:
I solved the problem by iteration.

Of all the math techniques for solving problems, iteration is about the most unpleasant.
Click to expand...

You tell that to your PC.

Edit: doh - pg beat me to it.
 
Re: Re: Tough logarithm problem

rppa said:


Hmmm. Given the hindsight of the other attempts, let me see if there's another approach.

First, let's go with the suggestion of substitution of x = t/20, so t/4 = 5x and t/5 = 4x.

2^(5x) - 2^(4x) = 3.

Hmm. Let y = 2^x = 2^(t/20).

y^5 - y^4 = 3

Huh. That suggests factoring it as

y^4(y-1) = 3

but I don't see how that helps. Damn.

Does your textbook give an exact answer? Given that, we might be able to backtrack.
Click to expand...

Yeah, I got that too. Guess that's why it has five roots.

Any chance that the question, rather than the answer, is wrong, komencanto?
 
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