Expand log route x3/y2
Answers
Step-by-step explanation:
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Secondary School Math 5 points
Expand log
root x cube / root Y square
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aquialaska Virtuoso
Answer:
After expansion we get \frac{3}{2}\times log\,x-log\,y
Step-by-step explanation:
Given Expression:
log\,(\frac{\sqrt{x^3}}{\sqrt{y^2}})
We need to expand the given expression.
We use the following result,
log (a/b) = log a - log b
log\,a^n=n.log\,a
(x^a)^b=x^{ab}
Consider,
log\,(\frac{\sqrt{x^3}}{\sqrt{y^2}})
=log\,\sqrt{x^3}-log\,\sqrt{y^2}
=log\,(x^3)^{\frac{1}{2}}-log\,(y^2)^{\frac{1}{2}}
=log\,(x)^{3\times\frac{1}{2}}-log\,(y)^{2\times\frac{1}{2}}
=log\,(x)^{\frac{3}{2}}-log\,(y)^{1}
=\frac{3}{2}\times log\,x-log\,y
Therefore, After expansion we get \frac{3}{2}\times log\,x-log\,y
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erinna Ambitious
The expanded form of given expression is \dfrac{3}{2}\log x-\log y.
Step-by-step explanation:
Consider the given expression is
\log (\dfrac{\sqrt{x^3}}{\sqrt{y^2}})
Using the properties of exponents it can be written as
\log (\dfrac{(x^3)^{1/2}}{(y^2)^{1/2}}) [\because \sqrt{x}=x^{1/2}]
\log (\dfrac{x^{3/2}}{y}) [\because (x^m)^n=x^{mn}]
Using properties of log we get
\log x^{3/2}-\log y [\because \log (\dfrac{a}{b})=\log a-\log b]
\dfrac{3}{2}\log x-\log y [\because \log (a^b)=b\log a]
Therefore, the expanded form of given expression is \dfrac{3}{2}\log x-\log y.
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The value of log3 9 – log5 625 + log7 343 is
Step-by-step explanation:
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