Question

Given that log(2)3=x,log(2)5=y, and log(2)7=z express log(2)(15)/(7) in terms of x,y, and z.

Answer 1

To express log2(15/7) in terms of given variables x, y, and z, you use logarithmic properties to rewrite 15 as the product of 3 and 5 and then apply the division property, resulting in the expression (x + y) - z.

Step-by-step explanation:

To express log2(15/7) in terms of x, y, and z when given that log2(3) = x, log2(5) = y, and log2(7) = z, we can use the properties of logarithms:

• The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (logb(xy) = logb(x) + logb(y)).
• The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers (logb(x/y) = logb(x) - logb(y)).

First, we can rewrite 15 as the product of 3 and 5:

log2(15) = log2(3*5) = log2(3) + log2(5) = x + y

Next, we can express the given expression by applying the division property:

log2(15/7) = log2(15) - log2(7) = (x + y) - z

Therefore, log2(15/7) in terms of x, y, and z is (x + y) - z.