Question

Find the value of (35" x 3") = 729.​

Answer 1

Answer:

624

Step-by-step explanation:

Answer 2

Answer:

If 3^x=729, then what is x equal to?

Step-by-step explanation:

The given exponential equation can be transformed as follows using the properties of exponents:

(1.) 3^x = 729 (Given)

(2.) 3^x = 9³

But, 9 = 3²; therefore, substituting on the right side of equation (2.) for 9, we get:

(3.) 3^x = (3²)³

By the “Power of a Power” property of exponents, i.e., (bᵐ)ⁿ = bᵐⁿ, where b is a positive real number and m and n are any real numbers ¹, equation (3.) becomes:

(4.) 3^x = 3^6

By another property of exponents: “If b > 0, b ≠ 1, and m and n are real numbers, then bⁿ = bᵐ if and only if n = m,”² consequently, from equation (4.), we have as the value for x:

(5.) x = 6

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