Question

If logᵦ 2 = x and logᵦ 3 = y, evaluate the following in terms of x and y :

logᵦ 648

Answer 1

To evaluate logᵦ 648 in terms of x and y, we need to express 648 as a product, quotient, or power of the numbers 2 and 3. By expressing 648 as 6^4, we can simplify logᵦ 648 to 4x + 4y.

Step-by-step explanation:

To evaluate logᵦ 648 in terms of x and y, we need to express 648 as a product, quotient, or power of the numbers 2 and 3.

We know that logᵦ 2 = x, so 2 = ᵦx. Similarly, logᵦ 3 = y, so 3 = ᵦy.

Let's express 648 as a product of 2 and 3: 648 = 24 × 34 = (2 × 3)4 = 64.

Now, we can rewrite logᵦ 648 as logᵦ (24 × 34) = logᵦ (64).

Since 6 = 2 × 3, we can simplify the expression to 4 logᵦ 6. Finally, substituting the values of x and y, we get 4x + 4y.