Math, asked by kurakularamya2003, 1 month ago

expand logroot xsquare ysquare​

Answers

Answered by vggangster04
0

Answer:

there are a few things to

Answered by majumdararpu12345
0

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)

2

1

−log(y)

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

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