Discussion between SuperMan and barak manos

Stack Exchange

14:39

Partial answer: Note that: $\log(a)+\log(aq)+\log(aq^2)=\log(a\cdot aq\cdot aq^2)=\log(a^3q^3)=\log(aq)^3=3\log(aq)$ Therefore: $\log(a)+\log(aq)+\log(aq^2)=3\implies3\log(aq)=3\implies\log(aq)=1\implies aq=10$ Therefore: $a+aq+aq^2=62 \implies a+10+10q=62 \implies a=52-10q$ So now we have...

SuperMan

Thank you! Any ideas how to find a and q? :)

barak manos

@SuperMan: Well, for a start, $a+aq+aq^2=62 \implies a+10+10q=62 \implies a=52-10q$.

@SuperMan: So take that equation, and use equation given in the answer ($aq=10$) in order to get the exact values of $a$ and $q$.

SuperMan

Thank you very much!!! I appreciate it! Could I ask about another progression?

barak manos

@SuperMan: You're welcome. Please see updated answer for the full solution. A different question should be asked in a different post.

SuperMan

I saw it and solved the task! Thank you again! Got question about arithemtic progression and logarithm, should I make a new post?

barak manos

14:39

@SuperMan: Thank you for leading me to exactly 25,000 points :)

SuperMan

Hellol, can we talk here?

barak manos

Yes

But only for a short while, I'm at work...

SuperMan

Here is the short condition:
The logarithms of 4 positive numbers with base 2 make an arithmetic progression. The multiplication of it's first and last members is = -8 and the multiplication of the middle ones is = 0

Have to find those 4 numbers

barak manos

Please post it as a question, you'll get an answer pretty fast if you show what you've tried and you're having a problem with.

I don't see a quick solution here, there's some "wording" to do

Which is not possible in here (no LaTex parsing here)

SuperMan

Okay, thanks!

barak manos

14:47

Just make sure that you explain what part you're having difficulties with. People here don't like questions which seems like 'do my homework for me', so you should try to avoid leaving that impression.

SuperMan

But that is hard when you can't solve it even at 50%

barak manos

Surely you can show something

Denote the four numbers as a0, a1, a2, a3

The difference between them is d

SuperMan

yeah

barak manos

Sorry, the difference between their logarithms is d

a0*a3=-8

a1*a2=0