- #1

- 125

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## 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,