Question

Use properties of logarithms to condense each logarithmic expression. Where possible, evaluate logarithmic expressions without using a calculator.

Answer 1

We can use, mainly, the next properties of the logarithms:

`\log _b(m\cdot n)=\log _bm+\log _bn`
`\log _bm^r=r\log _bm`

Then, we have that:

1. First, we can use the previous property:

`\log _4v+\log _4w^5+\log _4x^2+\log _4u^{(1)/(3)}`

2. We can condense the first two terms using the first property:

`\log _4(v\cdot w^5)+\log _4x^2+\log _4u^{(1)/(3)}`

3. We can proceed similarly using the third term, and then the fourth term:

`\log _4(v\cdot w^5\cdot x^2)+log_4u^{(1)/(3)}`

4. Finally, we have that the con:

`\log _4(v\cdot w^5\cdot x^2\cdot u^{(1)/(3)})`