Question

Q: Given that log to base 2 of p= a, log to base 8 of q= b, and p/q=2^c, express c in terms of a and b.

Answer 1

To express c in terms of a and b, relate the given logarithmic equations and simplify the expression p/q = 2^c. The value of c is equal to a minus three times b.

Step-by-step explanation:

To express c in terms of a and b, we need to relate the given logarithmic equations and simplify the expression p/q = 2^c. Let's start by expressing the logarithmic equations in exponential form:

p = 2^a (equation 1)

q = 8^b (equation 2)

We can rewrite equation 2 as q = (2^3)^b, which simplifies to q = 2^(3b).

Now let's solve for c by substituting the exponential forms of p and q into the expression p/q = 2^c:

2^a / 2^(3b) = 2^c

Using the property of exponents that dividing two numbers with the same base subtracts their exponents, we get:

2^(a - 3b) = 2^c

Since the bases are equal, we can equate the exponents:

a - 3b = c

Therefore, c = a - 3b.