The examples below will teach you about expanding logarithms using the properties of logarithms.
Expanding logarithms is the inverse of simplifying logarithms. You are trying to express a single logarithm into many individual logarithms.
Example #1
Expand log_{5} (3xy)
Using the product property, log_{5} (3xy) = log_{5} 3 + log_{5} x + log_{5} y
Example #2
Expand log_{2} (5x / 10y)
Using a combination of the product property and the quotient property,
log_{2} (5x / 10y) = log_{2} (5x) - log_{2} (10y)
= log_{2} (5) + log_{2} (x) - [ log_{2} (10) + log_{2} (y) ]
= log_{2} (5) + log_{2} (x) - log_{2} (10) - log_{2} (y)
Example #3
Expand log (a^{2}b^{3})
Using a combination of the product property and the power property,
log_{10} (a^{2}b^{3}) = log_{10} a^{2} + log_{10} b^{3}
= 2log_{10} a + 2log_{10}
Example #4
Expand log3 [ √ (36x^{3}y) ]
Using a combination of the product property and the power property,
log3 [ √ (36x^{3}y) ] = log3 [ (36x^{3}y)^{1/2} ]
= 1/2 log3 (36x^{3}y)
= 1/2 [ log3 (36) + log3 (x^{3}) + log3 (y) ]
= 1/2 [ log3 (36) + 3log3 (x) + log3 (y) ]
= 1/2 log3 (36) + 3/2 log3 (x) + 1/2 log3 (y)
Dec 14, 18 04:05 PM
Here is how to convert square feet to acres - To convert square feet to ...
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Dec 14, 18 04:05 PM
Here is how to convert square feet to acres - To convert square feet to ...
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.