### Concept (1)

In mathematics, it can be useful limit the solution or even have multiple solutions for an inequality. For this we use a compound inequality, inequalities with multiple inequality signs. When solving compound inequalities, we use some of the same methods used in solving multi-step inequalities. The solutions to compound inequalities can be graphed on a number line, and can be expressed as intervals.

### Sample Problems (4)

Need help with "Product Rule of Logarithms" problems? Watch expert teachers solve similar problems to develop your skills.

Simplify:

log8(64x)
###### Problem 1
How to use the product rule for logarithms to expand a log.

Simplify:

log210 + log2(7 + x)
###### Problem 2
How to use the product rule for logarithms to condense a sum.

logbxy = logbx + logby

Tip: let m = logbx and n = logby
###### Problem 3
How to prove the product rule for logarithms.
###### Problem 4
Expanding, condensing, and simplifying logarithmic expressions using the logarithmic product rule.