Exponential and Log Functions

Solve Exponential Equations

100

Solve

3^(3x-5)>81

x>3

200

Solve

7^(6x)=7^(2x-20)

x=-5

300

Solve

9^(2x-1)=27^(x-4)

x=-10

400

Solve

3^(6x-5)<9^(4x-3)

x>1/2

500

Solve 

2^(3x-1)>=(1/8)^x

x>=1/6

Write Exponential Equations

100

Write the exponential equation of the function that passes through the points (0,1) and (-1,4).

y=1(1/4)^x

200

Write the exponential equation of the function that passes through the points (0,2) and (1,10).

y=2(5)^x

300

Write the exponential equation of the function that passes through the points (0,3) and (-1,6)

y=3(1/2)^x

400

Write the exponential equation of the function that passes through the points (0,4) and (1,12)

y=4(3)^x

500

Write the exponential equation of the function that passes through the points (0,1) and (-1,3)

y=1(1/3)^x

Exponential and Logarithm Forms

100

Write in logarithmic form

5^3=125

log_5 125=3

200

Write in logarithmic form

3^4=81

log_3 81=4

300

Write in logarithmic form

2^3=8

log_2 8=3

400

Write in exponential form

log_3 243=5

3^5=243

500

Write in exponential form

log_4 64=3

4^3=64

Properties of Logarithms

100

Simplify 

log_7 49

2

200

Combine

log_3 4+log_3 x

log_3(4x)

300

Combine

3log_2 x-2log_2 y

log_2(x^3/y^2)

400

Separate 

log_5((x^2y)/z^3)

2log_5 x+log_5 y-3log_5z

500

Separate 

log_7(a/(b^2c))

log_7a-2log_7b-log_7c

Solve Logarithms

100

Solve 

log_3 81=x

x=4

200

Solve 

log_3 3^(4x+3)=11

x=2

300

Solve 

4^(3x)=12

x=log12/(3log4)

400

Solve 

lnx+ln3=4

(e^4)/3

500

Solve 

e^(2x)+1=55

x=ln54/2