Question

How can I explain how to do this step by step using one of these three ways?1. logb mn = logb m + logb, n, by the Product Property2. logb m/n = logb m - log n, by the Quotient Property3. logb m^n = n logb m, by the Power PropertyWrite the expression as a single logarithm log2 5 - log23Expand the logarithm: log 4s^4t

Answer 1

From the problem, we have an expression of :

`\log _25-\log _23`

Note that the operation is subtraction so we will use the property of subtraction which is #2. Remember that Division and subtraction are related to each other and also multiplication with addition.

When subtracting logarithms with the same bases, you can express them by dividing the constant value of the logarithm.

As it states that :

`\log _bm-\log _bn=\log _b(m)/(n)`

Following the format of the expression, this will be :

`\log _25-\log _23=\log _2(5)/(3)`

The answer is :

`\log _2(5)/(3)`