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How do you condense #log r- log t- 2log s#?

Answer 1

Cora Alexander

#log(r/(ts^2))#

#"using the "color(blue)"laws of logarithms"#

#•color(white)(x)logx+logyhArrlog(xy)#

#•color(white)(x)logx-logyhArrlog(x/y)#

#•color(white)(x)logx^nhArrnlogx#

#rArrrlogr-(logt+logs^2)#

#=logr-log(ts^2)#

#=log(r/(ts^2))#

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Answer 2

Sadie Alexander

To condense ( \log r - \log t - 2\log s ), you can use the properties of logarithms, specifically the quotient rule and the power rule.

First, apply the quotient rule to combine the logarithms ( \log r ) and ( \log t ) into a single logarithm:

[ \log \left( \frac{r}{t} \right) ]

Then, apply the power rule to combine ( -2\log s ) into a single logarithm:

[ \log \left( s^{-2} \right) ]

Thus, condensing the expression yields:

[ \log \left( \frac{r}{t} \cdot s^{-2} \right) ]

Therefore, ( \log r - \log t - 2\log s ) condenses to ( \log \left( \frac{r}{t} \cdot s^{-2} \right) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.