Question

find the value of x (2) 5) -³×(2/5) ^18=(2/5)^10x​ pl

Answer 1

Step-by-step explanation:

I hope you understand this ans

Answer 2

SOLUTION

TO DETERMINE

The value of x when

$\displaystyle \sf{ { \bigg( \frac{2}{5} \bigg)}^{ - 3} \times { \bigg( \frac{2}{5} \bigg)}^{18} = { \bigg( \frac{2}{5} \bigg)}^{ 10x}}$

CONCEPT TO BE IMPLEMENTED

We are aware of the formula on indices that :

‌$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

‌$\displaystyle \sf{2. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

‌$\displaystyle \sf{3. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

‌$\displaystyle \sf{4. \: \: {a}^{0} = 1}$

EVALUATION

Here the given equation is

$\displaystyle \sf{ { \bigg( \frac{2}{5} \bigg)}^{ - 3} \times { \bigg( \frac{2}{5} \bigg)}^{18} = { \bigg( \frac{2}{5} \bigg)}^{ 10x}}$

We simplify it as below

$\displaystyle \sf{ { \bigg( \frac{2}{5} \bigg)}^{ - 3} \times { \bigg( \frac{2}{5} \bigg)}^{18} = { \bigg( \frac{2}{5} \bigg)}^{ 10x}}$

$\displaystyle \sf{ \implies { \bigg( \frac{2}{5} \bigg)}^{ - 3 + 18} = { \bigg( \frac{2}{5} \bigg)}^{ 10x}}$

$\displaystyle \sf{ \implies { \bigg( \frac{2}{5} \bigg)}^{ 15} = { \bigg( \frac{2}{5} \bigg)}^{ 10x}}$

$\displaystyle \sf{ \implies { \bigg( \frac{2}{5} \bigg)}^{ 10x} = { \bigg( \frac{2}{5} \bigg)}^{ 15}}$

$\displaystyle \sf{ \implies 10x = 15}$

$\displaystyle \sf{ \implies x = \frac{15}{10} }$

$\displaystyle \sf{ \implies x = \frac{3}{2} }$

FINAL ANSWER

Hence the required solution is

$\displaystyle \sf{ x = \frac{3}{2} }$

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