Question

find the value of x so that(2/5)3×(2/5)6=(2/5)3x​

Answer 1

Question:-

Find the value of x so that

$( \frac{2}{5} ) {}^{3} \times ( \frac{2}{5} ) {}^{6} = ( \frac{2}{5} ) {}^{3x}$

Solution:-

$( \frac{2}{5} ) {}^{3} \times ( \frac{2}{5} ) {}^{6} = ( \frac{2}{5} ) {}^{3x}$

Use the exponential identity

${x}^{m} \times {x}^{n} = {x}^{m + n}$

We get ,

$( \frac{2}{5} ) {}^{3 + 6} = ( \frac{2}{5} ) {}^{3x}$

$( \frac{2}{5} ) {}^{9} = ( \frac{2}{5} ) {}^{3x}$

$3x = 9$

$x = \frac{9}{3}$

$x = 3$

$\bf \: { \pink {answer : \: x \: = 3 }}$

Answer 2

Answer:

Question:-

Find the value of x so that

( \frac{2}{5} ) {}^{3} \times ( \frac{2}{5} ) {}^{6} = ( \frac{2}{5} ) {}^{3x}(

5

2

)

3

×(

5

2

)

6

=(

5

2

)

3x

Solution:-

( \frac{2}{5} ) {}^{3} \times ( \frac{2}{5} ) {}^{6} = ( \frac{2}{5} ) {}^{3x}(

5

2

)

3

×(

5

2

)

6

=(

5

2

)

3x

Use the exponential identity

{x}^{m} \times {x}^{n} = {x}^{m + n}x

m

×x

n

=x

m+n

We get ,

( \frac{2}{5} ) {}^{3 + 6} = ( \frac{2}{5} ) {}^{3x}(

5

2

)

3+6

=(

5

2

)

3x

( \frac{2}{5} ) {}^{9} = ( \frac{2}{5} ) {}^{3x}(

5

2

)

9

=(

5

2

)

3x

3x = 93x=9

x = \frac{9}{3}x=

3

9

x = 3x=3

\bf \: { \pink {answer : \: x \: = 3 }}answer:x=3

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