Discrete math logarithm problem

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Tayeeba

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hello,
Do you guys think I have done this right? I will appreciate your help :)IMG_1338.JPG
 
The second line in your working should be \(\displaystyle (ab)^4 = a\) not \(\displaystyle ab^4=a\).
 
Everything you've done looks good to me, and produces the same answer I get. However, I'd caution that your answer isn't the only answer. When you get to this step, you lose the other three potential answers:

\(\displaystyle b^4=1 \implies b=\left\{\pm 1, \: \pm i\right\}\)

Now, that said, I realize it's common for many classes to just outright ignore complex solutions, so if that describes your class, you're good to go.

EDIT: Oh shoot! Harry_the_cat is absolutely correct, I've made the same error in not seeing that it's really \(\displaystyle (ab)^4=a\). I'll leave my wrong post up for posterity's sake, because I still think the parts about complex solutions are worth acknowledging.
 
Last edited:
ksdhart2 said:
Everything you've done looks good to me, and produces the same answer I get. However, I'd caution that your answer isn't the only answer. When you get to this step, you lose the other three potential answers:

\(\displaystyle b^4=1 \implies b=\left\{\pm 1, \: \pm i\right\}\)

Now, that said, I realize it's common for many classes to just outright ignore complex solutions, so if that describes your class, you're good to go.
Click to expand...
You've missed the mistake in the second line of the supplied solution.
 
ksdhart2 said:
Everything you've done looks good to me, and produces the same answer I get. However, I'd caution that your answer isn't the only answer. When you get to this step, you lose the other three potential answers:

\(\displaystyle b^4=1 \implies b=\left\{\pm 1, \: \pm i\right\}\)

Now, that said, I realize it's common for many classes to just outright ignore complex solutions, so if that describes your class, you're good to go.

EDIT: Oh shoot! Harry_the_cat is absolutely correct, I've made the same error in not seeing that it's really \(\displaystyle (ab)^4=a\). I'll leave my wrong post up for posterity's sake, because I still think the parts about complex solutions are worth acknowledging.
Click to expand...

Thank you so much for your help. I tried to correct my mistake, and we didn't do complex logarithm in our class yet so I guess professor just wants a simple solution in this case.
 
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