Logarithms - The Easy Way!

This algebra 2 video tutorial provides a basic introduction of logarithms. It explains the process of evaluating logarithmic expressions without a calculator.

Log to Exponential Form:

Change of Base Formula:

Change of Base Log Problem:

Properties of Logarithms:

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Expanding Logarithmic Expressions:

Condensing Logarithmic Expressions:

Natural Logarithms:

Solving Exponential Equations:

Exponential Equations - Quadratic Form:

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Solving Logarithmic Equations:

Graphing Logarithmic Functions:

Graphing Exponential Functions:

Compound Interest Word Problems:

Logarithms Practice Problems:

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Final Exams and Video Playlists:

Full-Length Videos and Worksheets:

[newfire]

there's something with this guys' voice that makes me easier to understand the lesson

[justafan]

Funny how I didn’t understand this in a 1hour and 30 minute class but I can learn it in 10 minutes from this guy school is so useless

[jamesk]

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[lilahjohnson]

this is wild. I learned so much! My school's online learning site is such a waste of time. Why'd I just learn an entire unit in 10 mins. This is how education should be.

[astreroid]

The first 31 seconds of this video taught me more than what I understood in class. Thanks so much!

[Relge]

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[MikeMike-ycgg]

0:16 - FIRST EXAMPLE ---- " LOG _2 of 16 " is asking how many "2" s NEED to be MULTIPLIED to get to 16, here we see that 2x2x2x2 = 16
so therefore " LOG_ 2 of 16 = 4 " because we need to multiply four "2"s to get 16 .

1:11 - log _4 of 1 - " log" of 1 is ALWAYS equal to ZERO

1:19 - LOG _ 7 of 7 , when BOTH numbers are the same the simply "cancel out" and will ALWAYS equal to "1 "

1:36 - What to do if you're not given a base ?? ( in this case, LOG of 1000) ** if you're NOT GIVEN a base, the base is ALWAYS assumed to be a "10". with that in mind LOG (1000) becomes >>>> LOG _10 (1000) AND LOG _ 10 (1000) = 3., because 10x10x10 = 1000

2:17 - What about " LOG of 0.0001 " ??? * as previously discussed when we have no base its always assumed to be "10"
so LOG_10 (0.0001) = - 4 BECAUSE the " 1 " in " 0.0001 " is in the " ten thousandths " place and

10x10x10x10 = 10, 000 BUT we know its NOT " Ten THOUSAND " its " Ten THOUSANDTHS " so instead of 10^ 4 its 10^ - 4


2:35 - QUICK REVIEW, and noticing the logarithm pattern

LOG of 1 = 0
LOG (10) = 1
LOG (100 )= 2
LOG (1000) = 3
LOG (10, 000)= 4 *** notice how the number of "zeros" correlate with the number on the right ** for example " 10, 000" has
FOUR " zeros " and LOG of 10.000 = 4

so with that in mind whats " LOG of 1, 000, 000 " ?? well we know that "1, 000, 000 : has SIX "zeros" in it , so therefore  
" LOG of 1, 000, 000 = 6 "


3:28 - Logarithms with decimals ( further explained ) as discussed above the number of "zeros". directly correlate to the number on the "right"

so >>>>. LOG of 0.1 = - 1
LOG ( 0.01) = - 2
LOG ( 0.001) = - 3
LOG (0.0001) = - 4


4:04 - whats " 7 LOG _ 7 ( 38 ) ? , if you ever get this odd question on a test, SIMPLY CANCEL the two numbers out ( in this case we'll cancel the two 7's out ) and the answer will equal to the the other number ( in this case it will equal to = 38 ) so " 7 LOG _7 ( 38) becomes >>> LOG (38)
and LOG (38) = 38


4:51 - Working with fractions in a logarithm question EXAMPLE we know " log _ 3 of 9 = 2 " but how would our answer change if we had
LOG _ 3 ( 1/9 ) ?? Well, actually, "LOG _ 3 of ( 1/9) = -2 " * you have to flip the fraction( * *** And the NEGATIVE EXPONENT will cause
the "9" to move from the TOP to the BOTTOM ( 9/1 >>>> 1/9 )

5:35 - what if we flipped the numbers ?? if " Log _ 3 ( 9) = 2 " what's " Log 9 _ ( 3 ) " equal to ?? well SURPRISE SURPRISE there's a "2'" involved
" Log _ 9 ( 3 ) = 1/2 ) " * you have to move the "2 " from the TOP to the BOTTOM " ( 2/1 becomes >>> 1/2 )


5:54 -- whats " Log _ 9 ( 1/3 ) equal to ? well know that " Log _9 ( 3 ) = 1/2. (so knowing that we have to "flip" the fraction * turn 1/3 to 3/1 *
" Log _9 (1/3 ) = - 1/2 ** REMEMBER, a NEGATIVE exponent ALLOWS us to FLIP the fraction ***

6:06 - ANYTIME we have a fraction, our answer WILL be NEGATIVE, and anytime our "base" number is larger than the second number
EX : " Log _ 9 ( 3) our answer WILL be a FRACTION


6:44

7:07 - Review questions ( pause and try to answer questions )



8:57 - MORE practice questions . ( pause and try to answer questions )

[theviewer]

I got a test in 17 minutes 😂 thanks for the video.

[thedevilofhellskitchen]

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[rednas]

-.-
i am brainfarting that my teacher couldnt explain this to me and you did it in 1 min...
nice job ^^

[hicapasforlifeyeet]

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[hararazzaq]

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[A-arons_mclovinit]

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[Bonitopantera]

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[shandi.peitsch]

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[prateekchoudhary]

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[emasart]

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[Amed.khalid]

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[jess_amaris]

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[annieluo]

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