expand logroot xsquare ysquare
Answers
Answer:
there are a few things to
Answer:
After expansion we get \frac{3}{2}\times log\,x-log\,y
2
3
×logx−logy
Step-by-step explanation:
Given Expression:
log\,(\frac{\sqrt{x^3}}{\sqrt{y^2}})log(
y
2
x
3
)
We need to expand the given expression.
We use the following result,
log (a/b) = log a - log b
log\,a^n=n.log\,aloga
n
=n.loga
(x^a)^b=x^{ab}(x
a
)
b
=x
ab
Consider,
log\,(\frac{\sqrt{x^3}}{\sqrt{y^2}})log(
y
2
x
3
)
=log\,\sqrt{x^3}-log\,\sqrt{y^2}=log
x
3
−log
y
2
=log\,(x^3)^{\frac{1}{2}}-log\,(y^2)^{\frac{1}{2}}=log(x
3
)
2
1
−log(y
2
)
2
1
=log\,(x)^{3\times\frac{1}{2}}-log\,(y)^{2\times\frac{1}{2}}=log(x)
3×
2
1
−log(y)
2×
2
1
=log\,(x)^{\frac{3}{2}}-log\,(y)^{1}=log(x)
2
3
−log(y)
1
=\frac{3}{2}\times log\,x-log\,y=
2
3
×logx−logy
Therefore, After expansion we get \frac{3}{2}\times log\,x-log\,y
2
3
×logx−logy