Question

Condense into a single logarithm. Do not Evaluate

a) log5 4 - log5 16
b) log5 (4 * 16)
c) log5 (4 / 16)
d) log5 (4 + 16)

Answer 1

To condense logarithmic expressions, we can use the rules of difference and sum of logarithms.

Step-by-step explanation:

To condense logarithmic expressions, we can use the following rules:

1. The difference of logarithms is equal to the logarithm of the quotient.
2. The sum of logarithms is equal to the logarithm of the product.

a) Using the first rule, we have:

log5 4 - log5 16 = log5 (4/16)

b) Using the second rule, we have:

log5 (4 * 16) = log5 64

c) Using the first rule, we have:

log5 (4 / 16) = log5 (1/4)

d) This expression cannot be condensed further as the terms do not have any common logarithmic base.