PreCalc Chapter 4

Ch 4 Inverse, Exponential and Logarithmic Functions

Ch 4.1 Inverse Functions

Finding an Inverse Function From a Table
http://www.youtube.com/watch?v=TSztRfzmk0M&feature=youtu.be 

Finding Function and Inverse Function Values Using a Table
http://www.youtube.com/watch?v=o5GIiwVMo2o&feature=youtu.be

Finding Function and Inverse Function Values Using a Graph of f(x)
http://www.youtube.com/watch?v=FIF8SdZkJc8&feature=youtu.be

Determining if the Graph of a Relation is a One-to-One Function
http://www.youtube.com/watch?v=tbSGdcSN8RE&feature=youtu.be

Finding the Inverse of Function f(x)=(x+2)² by Restricting its Domain, and finding the Domain and Range of the Inverse Function
http://www.youtube.com/watch?v=rsJ14O5-KDw&feature=youtu.be

Definition of Inverse Functions ;
Finding the Inverse of f(x)=7+x, g(x)=5x, and h(x)=3x+2, and Verifying if they are the Correct Inverses ;
Finding the Domain and Range of the Function of f(x)=x²-3 for x≥0, its Inverse, and Domain and Range of the Inverse
http://www.youtube.com/watch?v=vLdAkKO79QA&list=PL554F9F460401DF50&index=99&feature=plpp_video

Definition of Inverse Functions ;
Determining if the Function is One-to-One from the Graph ;
Finding the Inverse of  f={(1,2), (-2,3),(5,2)};
Finding the Inverse of y=x³+2;
Finding the Inverse of y= 2 / x-4
http://www.youtube.com/watch?v=qgezKpQYH2w

Finding the Inverse of f(x)= 4x / x-2
http://www.youtube.com/watch?v=yOTLNg1QgOQ&list=PL554F9F460401DF50&index=98&feature=plpp_video

Finding the Domain and Range of Function f(x)=√2x-1 -3 and its Inverse
http://www.youtube.com/watch?v=eOn1yGvl17A&feature=youtu.be

Find the Inverse of the following Functions of f(x)= 4 / x+7

http://www.youtube.com/watch?v=Ib9ndr0TBz0&feature=plcp

f(x)= 5x+2 / x-3
http://www.youtube.com/watch?v=VEbJYAbSOxQ&feature=youtu.be

f(x)=⁶√x-2
http://www.youtube.com/watch?v=e0G3mWFy93U&feature=plcp

f(x)=5e^x+4
http://www.youtube.com/watch?v=6tboDrNWBfg&feature=plcp

Determining if f(x)=4x and g(x)= x/4 are Inverses ;
Determining if f(x)=2x+9 and g(x)= x/2 -9 are Inverses
http://www.youtube.com/watch?v=wrru-viN3x0&feature=youtu.be

Ch 4.2 Exponential Functions

Definition of Exponential Function;
Graphing y=2^x and y=(1/2)^x;
Solving 6 ^7-x=6^2x-1;
Solving 27^x-1 = 9^2x-3 ;
Graphing  y=(2/5)^x, y=(2/5)^x-3 ,  and y=(2/5)^x-3 ;
http://www.youtube.com/watch?v=KWr_Txv3t-E&list=PL554F9F460401DF50&index=97&feature=plpp_video

Finding the Function in the Form of f(x)=ab^x if the y-intercept is 6 and Contains the Point (2, 3/32);
Finding the Function in the Form of f(x)=ab^x+c if the y-intercept is 425, Horizontal Asymptote is y=72 and Contains the Point (1, 248.5);
Finding the Principal after 20 years if $1000 is Invested at a Rate of %7 per Year Compounded Monthly
http://www.youtube.com/watch?v=HrsH7o8lV7s&list=PL554F9F460401DF50&index=96&feature=plpp_video

Solving Exponential Equation 4^x=28
http://www.youtube.com/watch?v=lPRH6yyShUc&feature=plcp

Ch 4.3 The Natural Exponential Function

Using A=P(1+ r/n)^nt to Compute the Expression P(1+ r/n)^nt if $1 is Invested at 100% for One Year and if the Interest is Compounded Annually, Quarterly, Monthly, Daily, Hourly, Every Minute…;
Growth or Decay Graph, y-intercept, Horizontal Asymptote, Range and Domain of Natural Exponential Function y=e^x;
Using Compounded Continuously Interest Formula A=Pe^rt to find the Amount if Invested $100 at 12.5% for 10 years Compounded Continuously ;
Finding the Interest Rate if the Amount $890.20 is Received from Invested $400 for 16 years Compounded Continuously
http://www.youtube.com/watch?v=tbMmhvR8_7k&list=PL554F9F460401DF50&index=93&feature=plpp_video

Finding the Zeros of f(x)= -x²e^-x+2xe^-x
http://www.youtube.com/watch?v=PzoXpmge5tU&list=PL554F9F460401DF50&index=92&feature=plpp_video

Ch 4.4 Logarithmic Functions

Finding the Inverse of f(x)=5^x;
Writing  log₈64=2, log₁₆4= 1/2, log_q7=t, log_x+2(a² = b²)=st in Exponential Form ;
Writing 27^1/3=3,   10²=100 , x^a=12,(a+b)^7x=84x+y in Logarithmic Form ;
Writing the Meaning of and Evaluating log₁₀1000, log₂8, log₉3, log₈(-5),log₈ 1;
Properties of Logarithms  log_a 1, log_aa ,  log_aa^x, a^log_ax;
Solving log₅x = log₅7
http://www.youtube.com/watch?v=lHxURcbyYDo&list=PL554F9F460401DF50&index=95&feature=plpp_video

Converting Logarithm log₄64 into an Exponential Form
http://www.youtube.com/watch?v=bwme8iCJjPA&feature=plcp

Solving 3a^4t=10 for t ;
Solving L=Ma^t/n-p for t ;
Solving log₃(x+4)=log₃(1-x);
Solving log₇(x-5)=log₇(6x);
Solving x²=-4;
Solving e^xln2=0.25;
Solving 10^-4=x²;
Solving (e^ln2)^x= 1/4;
Graphing y=logx;
Graphing y=logx+2 and y=log(x+5) from y=logx
http://www.youtube.com/watch?v=j2wo1E5yrew&list=PL554F9F460401DF50&index=94&feature=plpp_video

Solving log₄6=x ;
Solving log₂(1/16)=x;
Solving log₅x=3;
Solving log_x81=4
http://www.youtube.com/watch?v=NjF8XdaC9sM&feature=youtu.be

Solving log₃(5x-3)=4;
Solving log₂(x²)=5
http://www.youtube.com/watch?v=a2BLBmUyGxA&feature=youtu.be

Solving log₄(2x-4)=2;
Solving log₂(x²-2x)=3
http://www.youtube.com/watch?v=WA6Dahb2s5U&feature=youtu.be

Solving 2log₅x-10=-6;
Solving -3log_x32+8=-7;
Solving 4log₃81-12=4x
http://www.youtube.com/watch?v=nrNaxeKXxqU&feature=youtu.be

Solving ln(2x-1)=5;
Solving 2log(x-2)+3=7
http://www.youtube.com/watch?v=Lz50yWogWC4&feature=youtu.be

Solving (log₅(log₅x))=-1
http://www.youtube.com/watch?v=xqFimHZWqq0&feature=youtu.be

Finding Exponential Decay Function with Logarithms
http://www.youtube.com/watch?v=Y7r0cl6X6mU&feature=youtu.be

Finding Exponential Decay Function and Half-life of a Sample
http://www.youtube.com/watch?v=D1mnrvbJEWs&feature=youtu.be

Finding Initial Amount of Exponential Decay Function given Half-life
http://www.youtube.com/watch?v=tALUq5t1yeY&feature=youtu.be

Ch 4.5 Properties of Logarithms

Determining if the Following are True or False : log(2·5)=(log2)(log5)
log(2·5)=log2+log5;  log(100+10)=log100+log10; log(10³)=log(10) ³; log(100/10)=log100/log10 ;  log(100/10)=log100-log10; log(100-10)=log100-log10; log(10³)=3log10;
Simplifying  log_a(uv);log_au^c; log_a(u/v); log_a(u ± v);
Expressing log_a x²y³/a²√z in Terms of Logarithms of x, y, z ;
Writing the  1/2 log_a(x²-1)-log_ac-5log_am as One Logarithm ;
Solving  log₂(x)-log₂(x+2)=3;
Solving log₄(3x+2)=log₄15
http://www.youtube.com/watch?v=PCPdyAACLtI&list=PL554F9F460401DF50&index=91&feature=plpp_video

Expressing log x³y/w²z in Terms of Logarithm of x, y,z  or w
http://www.youtube.com/watch?v=JzVf_S8FUo8&feature=plcp

Writing the following Expressions as One Logarithm

1/2logx+3logy-4logx

http://www.youtube.com/watch?v=vvaK0mXlbsI&feature=plcp

logx-2[log(x-5)+log(x+2)]

http://www.youtube.com/watch?v=cfQca_dH5P0&feature=plcp

Solving Logarithmic Equation

log(x)+log(x-21)=2

http://www.youtube.com/watch?v=b8oAT8uYUs4&feature=plcp

Solving log₅12=log₅(2x-3);
Solving log₇(x²-3x)-log₇(10)=0;
Solving 2 log₃(3x)=6;
Solving log₅(x-2)+log₅(x+2)=1;
Solving lob₁₆(x)+log₁₆(x-1)=1/4
http://www.youtube.com/watch?v=ZUREfaCqWzY

Solving log(x+5)=log(x)+log(5);
Solving ln(x)+ln(x-4)+ln(3x)
http://www.youtube.com/watch?v=QauP7mOTgDs&feature=youtu.be

Solving log(x+4)-log(x+2)=2
http://www.youtube.com/watch?v=ZQqwpQIRqlk&feature=youtu.be

Solving log(x)+log(x+4)=2
http://www.youtube.com/watch?v=oEvSpOt0ass&feature=youtu.be

Solving log₂(x²)-log₂(x+4)=3
http://www.youtube.com/watch?v=TWypOVHtxDU&feature=youtu.be

Solving ln(x)+ln(x+6)= 1/2 ln(9);
Solving log₂(x+3)=log₂(x-3)+log₃9+4^log₄3
http://www.youtube.com/watch?v=6bVSJk0R9BQ&list=PL554F9F460401DF50&index=90&feature=plpp_video

Solving ln(x)=2[ln(a)+ln(b)]+4ln(b⁴)+3{ln(b)-ln(a)] for x in terms of a and b
http://www.youtube.com/watch?v=bU6Z61aPKhY&feature=youtu.be

Ch 4.6 Exponential and logarithmic Equations

Solving  7⁶-1=4;
Solving  3·2^x-2=13;
Solving  (2/3)^x=5^3-x;
Solving  5^x-3= 3^2x+1;
http://www.youtube.com/watch?v=5R5mKpLsfYg

Solving  5^x=78;
Solving 10-2x= 2/3
http://www.youtube.com/watch?v=kok95wKLquE&feature=youtu.be

Solving  3^x/4=10;
Solving 2^-x/5=61
http://www.youtube.com/watch?v=3rjMvow9wRo&feature=youtu.be

Solving  7^4x+1=128;
Solving e^2x-5=61
http://www.youtube.com/watch?v=6YtWTfAYLkw&feature=youtu.be

Approximating log₂20 to 4 Decimal Places ;
Solving  4^2x+3=5^x-2;
Solving log(5x+1)-log(2x-3)=2
http://www.youtube.com/watch?v=Q0ui7-o2dNI&list=PL554F9F460401DF50&index=89&feature=plpp_video

Solving 3^2x-3=5^4x+5
http://www.youtube.com/watch?v=8TH-8bZbZQs&feature=youtu.be

Solving 5(1.05)^x=7(1.12)^x
http://www.youtube.com/watch?v=wRI6CMYjxPc&feature=youtu.be

Solving log₁₆(x)-log₁₆(x-1)=1/4
http://www.youtube.com/watch?v=ZUREfaCqWzY (Last Part of the Video)

Solving the Equation 4(2^6x)=128
http://www.youtube.com/watch?v=RrWQI76NCPo&feature=plcp

Solving  2^x-6·2^-x=6;
Solving y= 10^x-10^-x / 2 for x
http://www.youtube.com/watch?v=P9P6exeQrr0&list=PL554F9F460401DF50&index=88&feature=plpp_video

Solving y= e^x-e^-x /e^x+e^-x  for x
http://www.youtube.com/watch?v=lpL7z12ijDE&list=PL554F9F460401DF50&index=87&feature=plpp_video