Question

find the value of x, if (6/5)^x × (5/6)^-2x = 125/216
PLEASE FAST ⏩
AND THE ANSWER IS = -1​

Answer 1

Step-by-step explanation:

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Answer 2

The value of x that satisfies the equation is approximately -1.

We can simplify the left-hand side of the equation using the properties of exponents:

$6/5^{x} \times 5/6^{-2x} = [(6/5^{1/5} ]^{5x} \times [(5/6^{-1/6} ]^{-12x} )$

$=6/5^{5x/5} \times 6/5^{-2x} = 6/5^{3x/5}$

So our equation becomes:

$6/5^{3x/5} = 125/216$

Taking the natural logarithm of both sides, we get:

ln$In 6/5^{3x/5} = In (125/216)$

Using the rule that ln$(a^b)$ = b ln(a), we can simplify the left-hand side:

(3x/5) ln(6/5) = ln(125/216)

Now we can solve for x:

$3x/5 = ln(125/216) / ln(6/5)$

$x = (5/3) ln(125/216) / ln(6/5)$

Using a calculator, we get:

x ≈ -1

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