Question

Discuss the following equation and determine whether it is true for all possible values of the variables. (Ignore values of the variables for which any term is undefined.) log₅(a/b²)log₅a-2log₅b True or False

Answer 1

The equation log₅(a/b²)log₅a-2log₅b simplifies to log₅(a³b) and is true for all possible values of the variables.

Step-by-step explanation:

The given equation is:

log₅(a/b²)log₅a-2log₅b

To determine whether this equation is true for all possible values of the variables, we can simplify it using logarithmic properties.

First, we can use the property log₋a-log₋c = log₅(a/b) to rewrite the equation as:

log₅(a/b²) + log₅a - 2log₅b

Next, we can use the property log₅a + log₅b = log₅(ab) to combine the terms:

log₅((a/b²)(ab²))

Simplifying further, we have:

log₅(a³b)

Therefore, the given equation simplifies to log₅(a³b) and is true for all possible values of the variables.

Learn more about Logarithmic properties