Simplifying a Log?

knpoe03

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Apr 13, 2020
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Hello!

I'm a bit confused by this question in my math homework. It instructs me to simplify out an equation so that the result does not contain a log. I've attempted to start this, but I'm really not sure if what I am doing is correct or even close to what I should be doing. I'd appreciate your help!

Screenshot 2020-11-21 at 10.52.54 AM - Edited.png
 

tkhunny

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No. log(x+p) = log(x+p) No log simplification, there. This is not an application of the Distributive Property.

log(x+p) + log(x+q) = log((x+p)(x+q)) -- Turns addition outside the logarithm function into multiplication inside the logarithm function.

You did this part well: log(p) + log(q) = log(pq)...except that you never should have been here. Apply this concept consistently and from the beginning.
 

Dr.Peterson

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Hello!

I'm a bit confused by this question in my math homework. It instructs me to simplify out an equation so that the result does not contain a log. I've attempted to start this, but I'm really not sure if what I am doing is correct or even close to what I should be doing. I'd appreciate your help!

View attachment 23255
Changing it to not contain a logarithm means changing a logarithmic equation to an exponential equation.
 

Subhotosh Khan

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Hello!

I'm a bit confused by this question in my math homework. It instructs me to simplify out an equation so that the result does not contain a log. I've attempted to start this, but I'm really not sure if what I am doing is correct or even close to what I should be doing. I'd appreciate your help!

View attachment 23255
1605978561432.png
Combine the two logs in the left-hand-side using properties of "log".

logb(x+p) + logb(x+q) \(\displaystyle \ \to \ \ \) logb[(x+p)*(x+q)]​

So now you have:

logb[(x+p)*(x+q)] = a​

Now eliminate "log" by using "exponential" (power) according to the definition of logarithm.
 

knpoe03

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Apr 13, 2020
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View attachment 23256
Combine the two logs in the left-hand-side using properties of "log".

logb(x+p) + logb(x+q) \(\displaystyle \ \to \ \ \) logb[(x+p)*(x+q)]​

So now you have:

logb[(x+p)*(x+q)] = a​

Now eliminate "log" by using "exponential" (power) according to the definition of logarithm.
So, to eliminate the log by using exponents, I would use b^n=m. This would change the equation to b^a=(x+q)(x+p). Is this correct?
 

knpoe03

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Changing it to not contain a logarithm means changing a logarithmic equation to an exponential equation.
So to change it to an exponential function, I would use b^n=m. I got b^a=(x+p)(x+q). Is this correct? I'm not entirely familiar (or comfortable) with logs, so I appreciate any help you can offer.
 

knpoe03

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Apr 13, 2020
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No. log(x+p) = log(x+p) No log simplification, there. This is not an application of the Distributive Property.

log(x+p) + log(x+q) = log((x+p)(x+q)) -- Turns addition outside the logarithm function into multiplication inside the logarithm function.

You did this part well: log(p) + log(q) = log(pq)...except that you never should have been here. Apply this concept consistently and from the beginning.
Thanks for your response! I now see where I went wrong.
 

Harry_the_cat

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Mar 16, 2016
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So to change it to an exponential function, I would use b^n=m. I got b^a=(x+p)(x+q). Is this correct? I'm not entirely familiar (or comfortable) with logs, so I appreciate any help you can offer.
Yes that's correct. Well done!
 
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