Solve Log Law Problems Homework Statement

[AbsoluteZer0]

Homework Statement

Write as a single logarithm:

Homework Equations

Logarithm Laws:

log_a(xy) = log_a(x) + log_a(y)

log_a(\frac{x}{y}) = log_a(x) - log_a(y)
___________

Problem Set:

log_{10}A + log_{10}B - log_{10}C

\frac{1}{2}logX - 2log4

2logN + 3logX

The Attempt at a Solution

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

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

log_{10}{\frac{1}{2}X} - log_{10}8

to get log_{10}(\frac{0.5x}{8})

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:

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

Thanks,

 

[jedishrfu]

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.

 

[Tanya Sharma]

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

Yes..Thats right.

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

log_{10}{\frac{1}{2}X} - log_{10}8

to get log_{10}(\frac{0.5x}{8})

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:

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

Thanks,

That is not the correct way .

Use the following property of logarithms : log_b(xⁿ) = n log_bx.

 

[AbsoluteZer0]

I solved the second one to:

log_{10}\frac{X^{0.5}}{16}

Is this correct?

Thanks

 

[Tanya Sharma]

I solved the second one to:

log_{10}\frac{X^{0.5}}{16}

Is this correct?

Thanks

Correct

 

[AbsoluteZer0]

And would the second one be

log_{10}(N^2X^3)?

Thanks

 

[Tanya Sharma]

And would the second one be

log_{10}(N^2X^3)?

Thanks

:thumbs:

 

[AbsoluteZer0]

Thank you very much!

 

[jedishrfu]

dont forget to use the Thanks button to thank everyone.