Question

if (2/5)^3*(2/5)^7=(2/5)^2x then find x​

Answer 1

Answer:

The value of x is 11

Step-by-step explanation:

Given : (2x +3) : (3x +2) = 5:7

To find : Value of x

Solution :

(2x +3) : (3x +2) = 5:7(2x+3):(3x+2)=5:7

\frac{2x+3}{3x+2}=\frac{5}{7}

3x+2

2x+3

=

7

5

7(2x+3)=5(3x+2)7(2x+3)=5(3x+2)

14x+21=15x+1014x+21=15x+10

21-10=15x-14x21−10=15x−14x

11=x

Hence The value of x is 11

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

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

$2. \sf \: { \: {a}^{m} = {a}^{n} \: } \: implies \: \: m = n$

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

GIVEN

$\sf{ \displaystyle \: \: { \bigg( \: \frac{2}{5} \bigg)}^{3} \times { \bigg( \: \frac{2}{5} \bigg)}^{7} = { \bigg( \: \frac{2}{5} \bigg)}^{2x} \: }$

TO DETERMINE

The value of x

EVALUATION

$\sf{ \displaystyle \: \: { \bigg( \: \frac{2}{5} \bigg)}^{3} \times { \bigg( \: \frac{2}{5} \bigg)}^{7} = { \bigg( \: \frac{2}{5} \bigg)}^{2x} \: }$

$\implies \: \sf{ \displaystyle \: \: { \bigg( \: \frac{2}{5} \bigg)}^{3 + 7} = { \bigg( \: \frac{2}{5} \bigg)}^{2x} \: }$

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

$\implies \: \sf{ \displaystyle \: 2x = 10\: }$

$\implies \: \sf{ \displaystyle \: x = 5\: }$

RESULT

$\boxed{\sf{ \: \:x = 5 \: \: }}$