fofopausiomiava

2022-09-04

Write the expression in terms of $\mathrm{log}x$ and $\mathrm{log}y$

$$\mathrm{log}{\textstyle (}\frac{{x}^{3}}{10y}{\textstyle )}$$

To be honest, I'm really unsure as to how the final answer should look like. In other words, what is the question asking for, and how do I go about getting there?

Any ideas would be appreciated.

$$\mathrm{log}{\textstyle (}\frac{{x}^{3}}{10y}{\textstyle )}$$

To be honest, I'm really unsure as to how the final answer should look like. In other words, what is the question asking for, and how do I go about getting there?

Any ideas would be appreciated.

Houston Ellis

Beginner2022-09-05Added 4 answers

Hint:

$$\mathrm{log}\left(\frac{{x}^{3}}{10y}\right)=\mathrm{log}\left({x}^{3}\right)-\mathrm{log}(10\cdot y)$$

You can use additional properties of logarithms until you get $\mathrm{log}x$ and $\mathrm{log}y$ to appear in your answer. You will need one application each of the properties

$$\mathrm{log}\left({a}^{n}\right)=n\mathrm{log}\left(a\right)\phantom{\rule{0ex}{0ex}}\mathrm{log}\left(ab\right)=\mathrm{log}\left(a\right)+\mathrm{log}\left(b\right)$$

$$\mathrm{log}\left(\frac{{x}^{3}}{10y}\right)=\mathrm{log}\left({x}^{3}\right)-\mathrm{log}(10\cdot y)$$

You can use additional properties of logarithms until you get $\mathrm{log}x$ and $\mathrm{log}y$ to appear in your answer. You will need one application each of the properties

$$\mathrm{log}\left({a}^{n}\right)=n\mathrm{log}\left(a\right)\phantom{\rule{0ex}{0ex}}\mathrm{log}\left(ab\right)=\mathrm{log}\left(a\right)+\mathrm{log}\left(b\right)$$

Gunsaz

Beginner2022-09-06Added 3 answers

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