Question

What is the value of x if:

2^x · 3^x+1 = 3888

• A. 2
• B. 4
• C. 3
• D. 5

Hint:

Prime factorization is the fastest way to compare exponents in such equations.

Answer 1

The Correct Option is B

Step 1: Prime Factorization of 3888

First, we break down 3888 into its prime factors:

3888 ÷ 2 = 1944 1944 ÷ 2 = 972 972 ÷ 2 = 486 486 = 2 × 243 243 = 3⁵

Therefore:

3888 = 2⁴ × 3⁵

Step 2: Rewrite the Given Equation

The original equation is:

2^x · 3^x+1 = 2⁴ · 3⁵

Step 3: Equating Powers of Prime Factors

Since the bases are the same, we can equate their exponents:

• For base 2: x = 4
• For base 3: x + 1 = 5 ⇒ x = 4

Both give x = 4, which is consistent.

Step 4: Final Answer

The value of x is:

x = 4