Expanding and Condensing Logs

Learn how to Expand and Condense Logs in this free math video tutorial by Mario's Math Tutoring. We go through the expanding and condensing formulas for logs as well as some example problems.

0:15 Properties of logs for expanding and condensing
1:52 Expanding Logs examples
6:25 Condensing Logs examples

Get the worksheet above from my TpT store. 10 expanding and 10 condensing problems utilizing the product, quotient and power properties. Answer key is also provided.

* Organized List of My Video Lessons to Help You Raise Your Scores & Pass Your Class. Videos Arranged by Math Subject as well as by Chapter/Topic. (Bookmark the Link Below)

[MariosMathTutoring]

Practice what you learned in this video.
Get the worksheet from my TpT store with the link above.
10 expanding and 10 condensing problems utilizing the product, quotient and power properties. Answer key is also provided.

[mazrafniddu]

To be honest with you, you could be a great teacher if you're not already, your ways of teaching are very simple and understandable. I learned more from this video than I did in 2 weeks from my teacher.

[InkerousCitaRik]

This may have saved me for my math Exam tomorrow on logarithms! Thank you for explaining in detail hopefully I will succeed in passing my test

[michaelgrigsby]

I'm sharing this with my students to help them better understand the properties of logarithms. At the end of your first example I would emphasize that after bringing down the exponent of 2 in the second log to write out the final answer as

log_2 (5) + 2log_2 (x) + log_2 (y) - log_2 (3).

Likewise, in the last example where you expanded the logarithm at about 6:00, I would write out the answer so that the students know what the final result is after applying the power rule of logarithms:

1/2 log_7 (x) + log_7 (y) - 3 log_7 (z). Thank you for the video!

[molokomaleka]

Omg you are soooo good 🙌🏾🙌🏾I wish you were my math teacher 😭😭😭😭😩😩😩

[michaeljames]

math on youtube has really changed the game when it comes to learning.

[acatalepsia]

dude's done a video on every topic 😭cannot thank u enough dude

[Substance]

Great explanation of this concept I'm sure you're a great teacher!!

[Tinylongcatgaming]

Thank you so much man, i was absent and didn't take that lesson in school, you are a life saver❤

[Jake-zrfw]

Much love, Mario. U gettin ya boi through algebra 2.

[TheRolvaag]

Man I needed to watch this, thank you so much

Very clear, very concise

[taylorsymone]

Omg this was so much easier to understand than Khan Academy thank you so much!

[christopherschueverer]

Holy shit man, I can't express how much this helped me. Thank you!!!!

[colecruce]

I have a test retake tomorrow and after watching this video I'm finally ready for it

[graphene]

great explanation!!! thank you Mario.

[RafaelJaureguiCaball]

Question when you trying to bring down an expo den from an equestion let’s say like the continual compound interest formula what if that formula was actually like A = P2^(rt) now what base ling would you use?

[sarahshehu]

do you multiply the two new coefficients? for third ex of expansion

[upstudi-youribcoursemaster]

Hi Mario, we are from Upstudi, we hated to get your awesome videos license for our IB maths academy, is this possible. let me know how can we contact you.

[justabunga]

On log base 2 of (5x^2y/3), should the answer be Because, in log base 2 of x^2 and if you put in negative values and expand and write without absolute values, it would make that one undefined. If you write the absolute values usually for expanding even integer powers, it will be defined as long as the argument is not equal to 0 since putting in negative and/or positive values will still yield a positive value. By the way, abs stands for absolute value and the _ stands for the subscript for log base of whatever value.

[pjujrmp]

So log x^2 is 2 * log x, but is it the same if I say (log x) ^2 = 2 * log x?