LAWS OF LOGARITHM with solved examples.

Like exponents, logarithms have rules and laws that work the same way as the rules of exponents. It is important to note that the laws and rules of logarithms apply to logarithms of any base. However, the same base must be used throughout a calculation.
We can use laws and rules of logarithms to perform the following operations:
Changing logarithmic functions to exponential form.
Addition
Subtraction
Multiplication
Division
Expanding and condensing
Solving logarithmic equations.
Laws of logarithms
The logarithmic expressions can be written in different ways but under certain laws called laws of logarithms. These laws can be applied on any base, but during a calculation, the same base is used.
The four basic LAWS of logarithms include:
-The Product Rule Law
-The Quotient Rule Law
-The Power Rule Law
-Change of Base Rule Law
Although logarithms are taught in schools to simplify computation involving large numbers, they still have a significant role in our daily lives.
Here are some of these applications of logarithms:
We use logarithms to measure the acidity and alkalinity of chemical solutions.
Measurement of earthquake intensity is performed on the Richter scale using logarithms.
The level of noise is measured in dB (decibels) on a logarithmic scale.
Exponential processes such as the decay of ratio active isotopes, growth of bacteria, the spread of an epidemic in a population, and cooling of a dead body are analyzed using logarithms.
A logarithm is used to calculate the payment period of a loan.
In calculus, the logarithm is used to differentiate complex problems and determine the area under curves.
Watch the video to learn more about Logarithms.
SUBSCRIBE: youtube.com/@SchoolofMathematicsNigeria
STALK ME ON,
Facebook: m. schoolofmathematics.ng
Instagram: schoolofmathematics.ng
Tiktok: www.tiktok.com/@somnigeria
Twitter: somNigeria
#lawsoflogarithm #logarithm #mathematics #logarithmyoutube
SUB COUNT: 60

[@Somng]

Thanks for watching. Don't forget to like, comment and share the video if you learnt something.

[@davidibiyemi1308]

My SISTER, I admire you very much. A Lady teaching Maths. This is wonderful & fantastic, thank you very much for this enlightenment

[@Somng]

Thank you for your kind words 🤩

[@chimaths-class]

Great job

[@Somng]

Thank you 🤩

[@vibha.nidgundi2863]

Any from India 👇🏻 By the way nice teaching ❤

[@Somng]

Thanks for watching 🤩

[@yestheorygaming5316]

i think theres an error on law 7 because they should be a power at the top of b if I'm not wrong

[@RoszyPeterz]

Oh no, please confirm correctly. 🤩

[@djdanzo206]

im so happy to see us africans progress in the world of science , much especially a lady🙂

[@Somng]

You’re so kind. Thank you!!!! We pray to never relent too. 🥂

[@uchechidera7287]

I've got the answer to be 3Log³7 (base 3) or 5.313✅ Thanks for the teaching.

[@Somng]

Thanks for watching 🤩

[@VincentKamboyi-uk2my]

Thanks madam continue with same spirit, am getting more knowledge from your explanation God bless you.

[@Somng]

Thank you for watching 🤩

[@KellyKelly-m6z]

I really understood Nice teaching ❤❤❤❤

[@Somng]

Thanks for watching 🤩

[@ngenek5353]

Good work 👍

[@Somng]

Thank uou

[@JohnsonSaypoe]

Thanks for the excellent presentation.

[@Somng]

Thank you for watching 🤩

[@donsena2013]

Excellent presentation -- Would be interested in the derivations of the last two logarithmic relationships that were shown

[@Somng]

Thank you for watching 🤩 Oh, about the derivatives, I’d see to it.

[@Naomy-kb8st]

My role model l like mathematics so much best teacher

[@Somng]

This is such a kind thing to say, Naomi. I wish you the very best in learning Mathematics too. 🤩

[@donatusonwunaje4715]

Good job. Well done

[@Somng]

Thank you 🙌

[@user-sg4pg4iy5b]

Thank you so much Really learnt alot

[@Somng]

Thank you for watching

[@JacksonZulu-cs4jn]

Nice explanations

[@Somng]

Thanks for watching

[@ezraemmanuel6734]

I love this woman and the way she does her stuff

[@Somng]

You’re kind. Thank you.

[@user-tk3zr5td9i]

I really don't like logarithms, fortunately I found you madam, I'm now able to solve some questions on this topic Watching from Zambia

[@Somng]

Hello fellow African from Zim, thank you for your kind words. I’m glad you were able to solve some questions too 🤩

[@DanlyneNdreyam-di7vc]

Yeah so am I..... I really hate logarithms but now am happy coz I understand more clearly now ❤❤🙏🙏🙏thankyou so much

[@Somng]

You’re welcome 🤩 Thanks for watching.

[@mulbahkoquoi6345]

Thanks for the initiative beautiful ❤️

[@Somng]

Thank you Mulbah

[@RoszyPeterz]

👏🏾👏🏾

[@AeshiSaid-zm4rq]

How can you calculate 2log5+log36-log9.

[@RoszyPeterz]

Follow the multiplication and division rule.

[@RoszyPeterz]

Log (25*36)/9

[@wamemokgethi9920]

What is the answer for the homework

[@constantinhiganiro7205]

What is it log1 in base 7 =?0

[@TeboBusang]

Thanks a lot 😊

[@Somng]

Thank you for watching 🤩

[@nutty8610]

-log base 3 of 7 +4log base 3 of 7

[@RoszyPeterz]

Keep going. You have to still simplify as they have same base. 🤩

[@AllanLlano-qt5gq]

Best teacher

[@Somng]

Such a kind thing to say. Thank you. ☺️

[@Levintoh]

The answer is 4 Log 7 3

[@smthngstrange]

Thanks so much❤

[@Somng]

Thank you for watching 🤩

[@MosesTembo-bn6dq]

Good I like it nw what of you have equation log there where 8 and 4

[@Somng]

Hey Moses, I’m still trying to understand your question please.

[@MosesTembo-bn6dq]

I got it madam thank you I enjoy

[@ThankgodGodblesd]

Good afternoon please. What is induce form

[@Somng]

Good afternoon, “Mathematical induction is a common method for proving theorems about the positive integers, or just about any situation where one case depends on previous cases. Here's the basic idea, phrased in terms of integers: You have a conjecture that you think is true for every integer greater than 1.” I got this from google after typing your question. Kindly read more from there.

[@alphatwilz1098]

Next class pliz touch on functions

[@Somng]

Soon 🙌

[@AsahWangi]

❤

[@harrymatabal8448]

Mr user you say luckily you found her. But she's still lost

[@user-dv2eq8re9x]

thanks a lot

[@Somng]

Thanks for watching 🤩

[@vondasco1199]

I love the handwriting

[@Somng]

Thank you 🤩

[@user-wd8yj1pl2w]

Please can you do the homework for me to see Cox I still can't do it.?????

[@BesheaAbebe-2016E.C]

Continue

[@DavidSinyangwe-ri8mv]

You are awesome madam

[@Somng]

You’re so kind. Thank you for watching. 🤩

[@TaakaFoni]

😮😮😮

[@Somng]

What’s fascinating? 😅

[@BesheaAbebe-2016E.C]

Active female

[@culater]

Q T π

[@NnekaOkoli-pm9rx]

Nice teaching but I don't understand no 3

[@Somng]

Oh sorry about that. What do you need clarity on?

[@davies4870]

I'd like to know the exact answer, please

[@Somng]

Kindly tell us yours then we can check to see if you have a correction, that way you’d be able to learn better, yes?

[@davies4870]

@@Somng ok

[@davies4870]

@@Somng OK,-log base 3 of 7 +log 9 of 21-2log 3of 7

[@mahmudaminu3179]

Answer: -log7 base 3

[@RoszyPeterz]

Yaaay 🤩

[@user-sd4pu5km7h]

Lovely 😂

[@Mydatasciencejourney]

​@@RoszyPeterz Hi Rosy, how is that the answer? you need to make a video where you solved this problem. i got -3log7base3. how is -log7base3 the answer since the log7base1/3 will give us -log7base3, then 2log49base9 will give us 2log7base3 and the last which has -log(1/7)base squaroot of 3 will give use 2log7base3. for this last one 1/7 is 7 raised to power of -1 which made the log to have a positive sign the root 3 makes it to have 2log 7base 3. adding all the answer correctly it gives -3log7base3. i might be wrong though.

[@user-hl3eq7do8v]

It's explicit.

[@Somng]

Thanks for watching

[@thiyagarajahyogeswaranyoge3517]

6.1 and 6`1, 6x1, 6*1

[@Somng]

Try again 🥲

[@thiyagarajahyogeswaranyoge3517]

Six point one means 6+1/10. So write it different way for 6 into 1 as 6 x 1

[@ericaansah9352]

Pls i did not get the answer

[@Somng]

Send in your attempt let’s see

[@harrymatabal8448]

I beg to differ. Go and google up laws of logs. Yours is a derivation. There's a difference

[@Somng]

Okay. Thank you for watching 🤩

[@sureshchand6543]

I like your teaching keep up the great work.

[@Somng]

Thank you for watching 🤩

[@LahjaHomateni]

I understood everything but the homework is rough 😢

[@Somng]

Sorry about that. Maybe you should give it an attempt.

[@ericaansah9352]

Yes oo same here

[@ericaansah9352]

Yes oo same here

[@ericaansah9352]

Yes oo same here

[@ericaansah9352]

Yes oo same here

[@user-bn9pq3up3y]

Solve for x Logx3+logx27=2 (2*)²-3(2*)+2=0 Old can u help me

[@RoszyPeterz]

x = 9, if I read that correctly.

[@Wiserise4u]

😢😢😢😢😢😢😢

[@Somng]

What’s wrong? 😅

[@user-dn9nr9sd8t]

Your volume is very much low please

[@Somng]

We’d take that into consideration. Thanks for watching. 🤩

[@user-uq9vb5oq8j]

log7:⅓+2log49:9=-log7:3⅓

[@Somng]

Wow, I wish I could translate this. 😅

[@AllanLlano-qt5gq]

Best teacher

[@Somng]

Thank you 🤩