Question

How do you express log base 2 of 6 in terms of log base 2 of 3?

Answer 1

To express log base 2 of 6 in terms of log base 2 of 3, use the property of logarithms on the product 2*3. The result is 1 + log2(3) because log base 2 of 2 is equal to 1.

Step-by-step explanation:

To express log base 2 of 6 in terms of log base 2 of 3, we can use the fact that 6 is the product of 2 and 3. By the property of logarithms that states the logarithm of a product is equal to the sum of the logarithms (logb(xy) = logb(x) + logb(y)), we can write:

log2(6) = log2(2×3) = log2(2) + log2(3)

Now, since log2(2) is simply 1 (because 2 is the base and 21 = 2), we have:

log2(6) = 1 + log2(3)

So the expression for log base 2 of 6 in terms of log base 2 of 3 is:

1 + log2(3).