Question

if (2/5)^x=(5/2)^2 × (4/5) find the value of x​

Answer 1

Answer:

x = - 2

Step-by-step explanation:

Divide and conquer

1st term = $( 2 / 5 )^{x} = 2^x / 5^x$

2nd term = $( 5 / 2 )^2 = 5^2 / 2^2 = 25 / 4$

3rd term = 4 / 5

Now coming to the real solution,

$2^x / 5^x = 5^2 / 2^2 * 4 / 5\\\\2^x / 5^x = 5^2 / 2^2 * 2^2 / 5^1\\\\( 2^x / 5^x ) / ( 5^2 / 2^2 ) = 2^2 / 5^1\\\\( 2^x / 5^x ) * ( 2^2 / 5^2 ) = 2^2 / 5^1\\\\2^x * 2^2 / 5^x * 5^2 = 2^2 / 5^1\\\\2^{x + 2} / 5^{x + 2} = 2^2 / 5^1\\\\x + 2 / x + 2 = 2 / 1\\\\x + 2 / x + 2 = 2\\\\x + 2 = 2 ( x + 2 )\\\\x + 2 = 2x + 4\\\\2x - x = 2 - 4\\\\x = -2$

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