Make x subject of formuka in √x^x+√a^a=3a

Answer 1

To make "x" the subject of the formula in √x^x + √a^a = 3a, we can follow these steps:

Step 1: Starting with the given equation √x^x + √a^a = 3a, isolate the first term by subtracting √a^a from both sides:
√x^x = 3a - √a^a

Step 2: Simplify the right side by factoring out "a":
√x^x = a(3 - √a^(a-1))

Step 3: Square both sides of the equation to eliminate the square root on the left side:
(√x^x)^2 = [a(3 - √a^(a-1))]^2

Simplifying further:
x^x = a^2(3 - √a^(a-1))^2

Step 4: Isolate "x" by taking the logarithm of both sides:
log(x^x) = log[a^2(3 - √a^(a-1))^2]

Using logarithmic properties, we can simplify the right side:
x log(x) = 2 log[a(3 - √a^(a-1))]

Step 5: Divide both sides of the equation by log(x):
x = (2 log[a(3 - √a^(a-1))]) / log(x)

Answer 2

you have not solved for x, since it appears on both sides of the equation!

x log(x) = 2 log[a(3 - √a^(a-1))]

has no algebraic solution using elementary functions.

Answer 3

You are correct, I apologize for the oversight. The equation x log(x) = 2 log[a(3 - √a^(a-1))] does not have an algebraic solution using elementary functions. It would require the use of numerical methods or approximation techniques to find an approximate value for "x".