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:

$\log _4v+\log _4w^5+\log _4x^2+\log _4u^{\frac{1}{3}}$

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

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

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

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

4. Finally, we have that the con:

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