Product Rule

Reference > Algebra: Common Logarithms

Description

The Product Rule states that:

\(\log_{b}{(xy)}=\log_{b}{x}+\log_{b}{y}\)
Examples

Example 1 [Top]

\[\log_{2}{9}+\log_{2}{3}\]
1
Use Product Rule: \(\log_{b}{(xy)}=\log_{b}{x}+\log_{b}{y}\)
\[\log_{2}{(9\times 3)}\]

2
Simplify \(9\times 3\) to \(27\)
\[\log_{2}{27}\]

Done

Decimal Form: 4.754888


 

Example 2 [Top]

\[\log_{2}{2x}+\log_{2}{3y}\]
1
Use Product Rule: \(\log_{b}{(xy)}=\log_{b}{x}+\log_{b}{y}\)
\[\log_{2}{(2x\times 3y)}\]

2
Simplify \(2x\times 3y\) to \(6xy\)
\[\log_{2}{(6xy)}\]

Done


 

Example 3 [Top]

\[\log_{2}{5}+\log_{2}{3}+\log_{2}{7}\]
1
Use Product Rule: \(\log_{b}{(xy)}=\log_{b}{x}+\log_{b}{y}\)
\[\log_{2}{(5\times 3\times 7)}\]

2
Simplify \(5\times 3\times 7\) to \(105\)
\[\log_{2}{105}\]

Done

Decimal Form: 6.714246