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7^-2*3^2={3/4}^4x
Find x .

User Xierui
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Final answer:

To find the value of x in the equation 7^-2 * 3^2 = (3/4)^4x, we can simplify the left side of the equation and expand the right side. Cross multiplying and simplifying, we obtain the equation 9 * 2^8x = 49 * 3^4x. Equating the exponents, we solve for x to find x = 1/2.

Step-by-step explanation:

Given the expression 7-2 * 32 = (3/4)4x, we need to find the value of x.

To solve this, we can simplify the left side of the equation first. 7-2 means taking the reciprocal of 72, which is 1/72. 32 equals 9. So, the left side becomes (1/49) * 9.

Next, we can expand (3/4)4x by rewriting it as (34x) / (44x).

Now, equate the left and right sides of the equation and solve for x. (1/49) * 9 = (34x) / (44x).

Cross multiplying and simplifying, we get (1/49) * 9 * 44x = 34x.

By expressing 4 as 22, we can rewrite the equation as (1/49) * 9 * 28x = 34x.

Cancel out the common factors on both sides of the equation to obtain 9 * 28x = 49 * 34x.

Now, we can equate the exponents. 8x = 4x + 2.

Solving for x, subtract 4x from both sides of the equation to get 4x = 2.

Finally, divide both sides by 4 to find the value of x: x = 2/4 = 1/2.

User Ahinkle
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