# PreCalc Chapter 4

Ch 4 Inverse, Exponential and Logarithmic Functions

Ch 4.1 Inverse Functions

Finding an Inverse Function From a Table

Finding Function and Inverse Function Values Using a Table

Finding Function and Inverse Function Values Using a Graph of f(x)

Determining if the Graph of a Relation is a One-to-One Function

Finding the Inverse of Function f(x)=(x+2)² by Restricting its Domain, and finding the Domain and Range of the Inverse Function

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

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

Finding the Inverse of f(x)= 4x / x-2

Finding the Domain and Range of Function f(x)=√2x-1 -3 and its Inverse

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

f(x)= 5x+2 / x-3

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

Ch 4.2 Exponential Functions

Definition of Exponential Function;
Graphing y=2x and y=(1/2)x;
Solving 6 7-x=62x-1;
Solving 27x-1 = 92x-3 ;
Graphing  y=(2/5)x, y=(2/5)x-3 ,  and y=(2/5)x-3 ;

Finding the Function in the Form of f(x)=abx if the y-intercept is 6 and Contains the Point (2, 3/32);
Finding the Function in the Form of f(x)=abx+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

Solving Exponential Equation 4x=28

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=ex;
Using Compounded Continuously Interest Formula A=Pert 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

Finding the Zeros of f(x)= -x2e-x+2xe-x

Ch 4.4 Logarithmic Functions

Finding the Inverse of f(x)=5x;
Writing  log864=2, log164= 1/2, logq7=t, logx+2(a2 = b2)=st in Exponential Form ;
Writing 271/3=3,   10²=100 , xa=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  loga 1, logaa ,  logaax, alogax;
Solving log5x = log57

Converting Logarithm log464 into an Exponential Form

Solving 3a4t=10 for t ;
Solving L=Mat/n-p for t ;
Solving log3(x+4)=log3(1-x);
Solving log7(x-5)=log7(6x);
Solving x2=-4;
Solving exln2=0.25;
Solving 10-4=x2;
Solving (eln2)x= 1/4;
Graphing y=logx;
Graphing y=logx+2 and y=log(x+5) from y=logx

Solving log46=x ;
Solving log2(1/16)=x;
Solving log5x=3;
Solving logx81=4

Solving log3(5x-3)=4;
Solving log2(x2)=5

Solving log4(2x-4)=2;
Solving log2(x2-2x)=3

Solving 2log5x-10=-6;
Solving -3logx32+8=-7;
Solving 4log381-12=4x

Solving ln(2x-1)=5;
Solving 2log(x-2)+3=7

Solving (log5(log5x))=-1

Finding Exponential Decay Function with Logarithms

Finding Exponential Decay Function and Half-life of a Sample

Finding Initial Amount of Exponential Decay Function given Half-life

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  loga(uv);logauc; loga(u/v); loga(u ± v);
Expressing loga x²y³/a²√z in Terms of Logarithms of x, y, z ;
Writing the  1/2 loga(x²-1)-logac-5logam as One Logarithm ;
Solving  log2(x)-log2(x+2)=3;
Solving log4(3x+2)=log415

Expressing log x³y/w²z in Terms of Logarithm of x, y,z  or w

Writing the following Expressions as One Logarithm

1/2logx+3logy-4logx

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

Solving Logarithmic Equation

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

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

Solving log(x+5)=log(x)+log(5);
Solving ln(x)+ln(x-4)+ln(3x)

Solving log(x+4)-log(x+2)=2

Solving log(x)+log(x+4)=2

Solving log2(x²)-log2(x+4)=3

Solving ln(x)+ln(x+6)= 1/2 ln(9);
Solving log2(x+3)=log2(x-3)+log39+4log43

Solving ln(x)=2[ln(a)+ln(b)]+4ln(b4)+3{ln(b)-ln(a)] for x in terms of a and b

Ch 4.6 Exponential and logarithmic Equations

Solving  76-1=4;
Solving  3·2x-2=13;
Solving  (2/3)x=53-x;
Solving  5x-3= 32x+1;

Solving  5x=78;
Solving 10-2x= 2/3

Solving  3x/4=10;
Solving 2-x/5=61

Solving  74x+1=128;
Solving e2x-5=61

Approximating log220 to 4 Decimal Places ;
Solving  42x+3=5x-2;
Solving log(5x+1)-log(2x-3)=2

Solving 32x-3=54x+5

Solving 5(1.05)x=7(1.12)x