# Log Law Problems

## 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
Mentor

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

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

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 : logb(xn) = n logbx.

I solved the second one to:

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

Is this correct?

Thanks

I solved the second one to:

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

Is this correct?

Thanks

Correct

And would the second one be

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

Thanks

And would the second one be

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

Thanks

:thumbs:

1 person
Thank you very much!

jedishrfu
Mentor
dont forget to use the Thanks button to thank everyone.

1 person