Question

Find the value of x and y from the following:

2^x · 3^y = 144

Answer 1

Given: 2^x · 3^y = 144

Step-wise calculation:

1. Factorize 144 into primes:

144 = 2⁴ × 3²

2. Equate the bases and their exponents on both sides:

2^x × 3^y = 2⁴ × 3²

3. For the equality to hold, the exponents of 2 and 3 must be equal respectively:

x = 4, y = 2