Question

Expand the logarithm log64a5

1. 4log6a5
2. Log64-5log6a
3. Log64+5lig6a
4. Log64 • 5log•6a

Answer 1

3.
`\log_6 4+5\log_6 a`

Explanation:

Given:

The logarithm to expand is given as:

`\log_6 4a^5`

We use the following property of logarithm to expand it into sum of 2 logarithms:

`\log_b (xy)=\log_b x+\log_b y`

Therefore,

`\log_6 4a^5` =
`\log_6 4+\log_6 a^5`

Now, we further simplify the second logarithm using the following property:

`\log_b x^m=m\log_b x`

Therefore,
`\log_6 a^5=5\log_6 a`

This gives,

`\log_6 4a^5` =
`\log_6 4+5\log_6 a`

Therefore, the correct choice is choice 3.