Math III Chapter 7 Exponential and Logarithmic Functions

Natural Logarithmic Equations

100

Using A Calculator: Find the value of

ln15=x

x=2.71

200

Evaluate 

3e^(2x+1)=12

x=.193

300

Solve. Round to the nearest hundredth if necessary.

e^(2x)-4=0

x=0.6931

400

Solve the natural logarithmic equation:

-3+ln(2x-1)=-1

x=4.195

500

3+4ln(2x)=15

Solve the natural logarithmic equation?

x=10.043

Logarithmic Equations

100

Solve for x

Log_2(8)=x

x=3

200

What is the solution for x

log₅36=x-2

x=4.23

300

Solve each equation. Round to the nearest hundredth if necessary.

9-2log(2x+1)=25

x=-.49

400

Solve each equation. Round to the nearest hundredth if necessary.

log₃4+log₃(x+2)=log₃62

x=13.5 or x=27/2

500

Solve for x:

log_2(5x+1)=log_2(8)+log_2(2)

x=3

Condense/Expand

100

Use properties of logarithms to expand the following logarithmic expression:

log(5/12)^3

3log5-3log12

200

Using properties of Logarithms condense the following expression and SIMPLIFY AS MUCH as POSSIBLE:

log_2(6)+log_2(8/3)

log_2(16)

4

300

Expand the following natural logarithm:

ln(root(3)(x/y))

1/3lnx-1/3lny

400

Expand the following Logarithm and SIMPLIFY AS MUCH AS POSSIBLE:

log_6(36x^3)

2+3log_6x

500

Condense the following logarithmic expression:

1/3[5ln(x+5)-lnx-ln(x^2-16)]

ln(root3(((x+5)^5)/(x(x^2-16))))

or

ln((x+5)^(5/3)/(x^(1/3)(x^2-16)^(1/3)))

Random

100

Is the following Exponential Function: Growth OR Decay

y=100(1/3)^x

Decay 

200

log1=0

Is the following statement true or false?

True

300

Solve the following exponential equation:

3^(5x)+1=37

x=0.65

400

What is the parent function of f(x) and its transformations?

f(x)=-1/2log(x)+2

Parent function: log(x)

Reflection over x-axis

Compression(shrink) by a factor of 1/2

Vertical Shift up 2

500

Solve the following exponential equations:

10^(2x-1)=10^(3x+4)

x=-5