Question

(a/b)power x-2 = (b/a)power x-4 ​

Answer 1

Answer:

1

Step-by-step explanation:

(a/b)^x-2=(b/a)^x-4

(a/b)^x-2=(a/b)^-x+4

so x-2=-x+4

and 2x=6

so x=3

Answer 2

Answer: x = 3

.

Step-by-step explanation:

$(\frac{a}{b}) ^{x-2} =(\frac{b}{a})^{x-4}\\\\\frac{a^{x-2} }{b^{x-2} } =\frac{b^{x-4} }{a^{x-4} }\\\\a^{x-2}*a^{x-4}=b^{x-4}*b^{x-2}\\\\a^{x-2+x-4}= b^{x-4+x-2}\\\\a^{2x-6}=b^{2x-6}\\\\(\frac{a}{b}) ^{2x-6}=1 \\\\(\frac{a}{b}) ^{2x-6}=(\frac{a}{b})^{0}$

Since bases are equal so exponents must be equal.

So 2x - 6 = 0

=> 2x = 6

=> x = 3

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