Find the Value of x:  given 2^x × 3^x+4 = 7^x.

We will be simplifying the equation and logarithms to solve this.

Answer: The value of x in the given equation 2^x × 3^x+4 = 7^x is 28.4835 

Let's solve this step by step.

Explanation:

Given, 2^x × 3^x+4 = 7^x 

Apply logarithms (log) on both sides.

⇒ log(2^x × 3^x+4) = log(7^x)

⇒ log(2^x) + log(3^x+4) = log(7^x)  [Using log (ab) = log a + log b]

⇒ x log(2) + (x + 4) log(3) = x log(7)  [Since, log a^m = m log a]

⇒ x log(2) + x log(3) + 4log(3) = x log(7)

⇒ x [(log(7) -  log(2) - log(3)] = 4log(3)

⇒ x = 4log(3) / [(log(7) -  log(2) - log(3)]

Using the logarithm calculator, we have:

log(2) = 0.3010

log(3) = 0.4771

log(7) = 0.8451

Substituting the values above:

⇒ x = 4(0.4771) / [0.8451 -  0.3010 - 0.4771]

⇒ x = 1.9084 / [0.067]

⇒ x = 28.4835 

Thus, the value of x in the given equation 2^x × 3^x+4 = 7^x is 28.4835.