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Log Law Problems

  • #1
125
1

Homework Statement




Write as a single logarithm:


Homework Equations



Logarithm Laws:

[itex]log_a(xy) = log_a(x) + log_a(y)[/itex]

[itex]log_a(\frac{x}{y}) = log_a(x) - log_a(y)[/itex]
___________

Problem Set:

[itex]log_{10}A + log_{10}B - log_{10}C[/itex]

[itex]\frac{1}{2}logX - 2log4[/itex]

[itex]2logN + 3logX[/itex]

The Attempt at a Solution



I simplified the first question to [itex]log_{10}(\frac{AB}{C})[/itex] Am I correct?

I wasn't sure about how to approach the second question. I multiplied [itex]\frac{1}{2}[/itex] by [itex]X[/itex] and [itex]2[/itex] by [itex]4[/itex] and simplified as follows:

[itex]log_{10}{\frac{1}{2}X} - log_{10}8 [/itex]

to get [itex]log_{10}(\frac{0.5x}{8})[/itex]

I'm not sure if this is correct though.

If it is wrong, how would I solve it correctly?

For the third problem, I solved it to:

[itex]log_{10}[ (2n)(3x) ][/itex]

Thanks,
 

Answers and Replies

  • #2
11,685
5,254
Your AB/C is correct.

For the 1/2 log X you haven't listed the loglaw for it which is:

C * log (x) = log (x^C)

given that rework your answer.
 
  • #3
1,540
134
I simplified the first question to [itex]log_{10}(\frac{AB}{C})[/itex] Am I correct?
Yes..Thats right.

I wasn't sure about how to approach the second question. I multiplied [itex]\frac{1}{2}[/itex] by [itex]X[/itex] and [itex]2[/itex] by [itex]4[/itex] and simplified as follows:

[itex]log_{10}{\frac{1}{2}X} - log_{10}8 [/itex]

to get [itex]log_{10}(\frac{0.5x}{8})[/itex]

I'm not sure if this is correct though.

If it is wrong, how would I solve it correctly?

For the third problem, I solved it to:

[itex]log_{10}[ (2n)(3x) ][/itex]

Thanks,
That is not the correct way .

Use the following property of logarithms : logb(xn) = n logbx.
 
  • #4
125
1
I solved the second one to:

[itex]log_{10}\frac{X^{0.5}}{16}[/itex]

Is this correct?

Thanks
 
  • #5
1,540
134
I solved the second one to:

[itex]log_{10}\frac{X^{0.5}}{16}[/itex]

Is this correct?

Thanks
Correct
 
  • #6
125
1
And would the second one be

[itex]log_{10}(N^2X^3)[/itex]?

Thanks
 
  • #7
1,540
134
And would the second one be

[itex]log_{10}(N^2X^3)[/itex]?

Thanks
:thumbs:
 
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  • #8
125
1
Thank you very much!
 
  • #9
11,685
5,254
dont forget to use the Thanks button to thank everyone.
 
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