Question

Find if (2/3)^x . (2/3)^-2x =81/16

Answer 1

Step-by-step explanation:

${ \frac{2}{3} }^{x} \times { \frac{2}{ 3} }^{ - 2x} = { \frac{3}{2} }^{4}$

${ \frac{2}{3} }^{x - 2x} = { \frac{2}{3} }^{ - 4}$

${ \frac{2}{3} }^{ - x} = { \frac{2}{3} }^{ - 4}$

Because the bases are same , the powers will also be same.

$- x = - 4$

$x = 4$

Therefore, the value of x = 4

I hope it helps you. If you have any doubts, then don't hesitate to ask

Answer 2

Answer:

Answer:

The value of x is 4

Step-by-step explanation:

Given the equation

(\frac{2}{3})^x\times (\frac{3}{2})^{2x}=\frac{81}{16}(

3

2

)

x

×(

2

3

)

2x

=

16

81

\text{As, }x^a=\frac{1}{x^{-a}}As, x

a

=

x

−a

1

(\frac{3}{2})^{-x}\times (\frac{3}{2})^{2x}=\frac{81}{16}(

2

3

)

−x

×(

2

3

)

2x

=

16

81

\text{As, }x^a\times x^b=x^{a+b}As, x

a

×x

b

=x

a+b

(\frac{3}{2})^{-x+2x}=\frac{81}{16}(

2

3

)

−x+2x

=

16

81

(\frac{3}{2})^{x}=\frac{3^4}{2^4}(

2

3

)

x

=

2

4

3

4

(\frac{3}{2})^{x}=(\frac{3}{2})^4(

2

3

)

x

=(

2

3

)

4

Comparing both sides, we get

x=4

Hence, the value of x is 4