Laws of Logarithms and Exponential Notation (Due in 9 hours)

[firefly]

I can't quite figure this one out. I found an example of this online at http://uncw.edu/courses/mat111hb/EandL/logprop/logprop.html#sec2 but the example wasn't as complicated. Please help if you can! this is due my 9 pm my time tonight

Here is the problem:

Use the Laws of logarithms to rewrite the expression (Log1) in a form with no logarithm of a product, quotient or power.
After rewriting we have (log2)

with the constant A=
B=
C=

------------------------

so far I have:

1/2 log [(x^2+14)/(x^2+4)(x^3-2)^18]

I think A, B, and C are the exponents of each x...

 

[mmm4444bot]

I think A, B, and C are the exponents of each x Nope.

Properties needed:

(1) log(a/b) = log(a) - log(b)

(2) log(a*b) = log(a) + log(b)

(3) log(a^n) = n log(a)

Symbolic EG:

\(\displaystyle log \sqrt{\frac{x}{y \cdot z^n}}\)

Switch from radical notation to exponential notation.

\(\displaystyle log \left( \frac{x}{y \cdot z^n} \right)^{1/2}\)

Apply property (3).

\(\displaystyle \frac{1}{2} \cdot log \left( \frac{x}{y \cdot z^n} \right)\)

Apply property (1).

\(\displaystyle \frac{1}{2} \cdot [ log(x) \;-\; log(y \cdot z^n) ]\)

Apply property (2).

\(\displaystyle \frac{1}{2} \cdot [ log(x) \;-\; [log(y) \;+\; log(z^n)] ]\)

Apply property (3).

\(\displaystyle \frac{1}{2} \cdot [ log(x) \;-\; [log(y) \;+\; n \cdot log(z)] ]\)

Can you distribute and simplify this expression?

Your exercise goes the same way, to find A, B, and C.

 

[firefly]

okay, based on what you gave me:

log [x^2+14 / (x^2+4)(x^3-2)^18]^1/2

1/2 [log [x^2+14 / (x^2+4)(x^3-2)^18]]

1/2 [log [(x^2+14) - [log(x^2+4) + log(x^3-2)^18]]]

1/2 [log [(x^2+14) - [log(x^2+4) + 18*log(x^3-2)]]]

A=1/2, B= -1/2, and C= 9?

Am I way off....?

 

[mmm4444bot]

log [x^2+14 / (x^2+4)(x^3-2)^18]^1/2

1/2 [log [x^2+14 / (x^2+4)(x^3-2)^18]]

1/2 [log [(x^2+14) - [log(x^2+4) + log(x^3-2)^18]]]

1/2 [log [(x^2+14) - [log(x^2+4) + 18*log(x^3-2)]]] Why did you stop at this point?

If you completed the remaining simplification mentally (to obtain the given form with A, B, and C), it may explain why the sign is wrong on one of your answers. So, you're not way off; you have only a single sign error.

A=1/2, B= -1/2, and C= 9

 

[firefly]

Re:

1/2 [log [(x^2+14) - [log(x^2+4) + 18*log(x^3-2)]]] Why did you stop at this point?

If you completed the remaining simplification mentally (to obtain the given form with A, B, and C), it may explain why the sign is wrong on one of your answers. So, you're not way off; you have only a single sign error.

A=1/2, B= -1/2, and C= 9

yes C= -9 right? however I submitted the incorrect answer, C=9

lol. At least I know for future reference

 

[mmm4444bot]

C = -9 right? Correct.

however I submitted the incorrect answer, C=9 Why? You still have hours remaining before your deadline.

At least I know for future reference Writing down each step is a good habit, even for experienced people. When I take mental shortcuts, I often create extra work for myself.