Question

if a^1-2x . b^1+2x =a^4+x . b^4-x then x log b/a ​

Answer 1

The value of x log(b/a) = log(ab)

Given:

$a^{1 - 2x} . b^{1 + 2x} = a^{4+x} . b^{4-x}$

To find:

Value of x(log(b/a))

Solution:

According to the given data,

$a^{1 - 2x} . b^{1 + 2x} = a^{4+x} . b^{4-x}$

=> $\frac{a^{1 - 2x} . b^{1 + 2x}}{a^{4+x} . b^{4-x}} - 1$

=>$a^{-(3x + 3)} . b^{3x - 3} = 1$

=> $a^{3x + 3} = b^{3x - 3}$

Taking the log of both sides,

3(x + 1) log a = 3(x - 1) log b

=> (x - 1) log b = (x + 1) log a

=>x log b - log b = x log a + log a

=>x(log b - log a) = log a + log b

Using the quotient rule and product rule of logarithmic functions, the equation can be written as

x log(b/a) = log(ab)

Hence, x log(b/a) = log(ab)

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