Exponential and Logarithmic Functions

Condense/Expand Logs

100

Expand: 

logxy^2

logx+2logy

200

Condense: 

3loga+1/2logb

loga^3sqrtb

300

Expand 

ln((x^4y)/sqrtz)

4lnx+lny-1/2lnz

400

Condense:

3log_2d-log_2e-4log_2f+1/3log_2g

log_2((d^3g^(1/3))/(ef^4))

500

Expand: 

log((7x^4y^2)/(5root6(z)))

log7+4logx+2logy-log5-1/6logz

Solving Exponential Equations 1

100

4^x=64

x=3

200

e^x=10

x=2.303

300

2^-x+1=6

x=-log_(2)5=-2.322

400

1/3e^x+1=5

x=ln(12)=2.485

500

-3e^-x-4=-13

x=-ln3==1.099

Solving Exponential Equations 2

100

3^(4x)=3^(2x-8)

x=-4

200

3^(2x)=9^(x+2

No solution

300

4^(2x)=16^(3x+2)

x=-1

400

2^(5x-2)=32^(2x-3)

x=13/5

500

4^(x+7)=8^(2x-12)

x=25/2

Solving Logarithmic Equations 1

100

log(6x+2)=log(18x-22)

x=2

200

log_3(x-4)=log_(3)2x

No solution (x=-4 is extraneous)

300

ln(2x+1)-ln(-4x+10)=0

x=3/2

400

logx^2=log(-2x+8)

x=-4, 2

500

log_2(-x^2+7)=log_2(3x)

x=1.541

Solving Logarithmic Equations 2

100

log_2x=3

x=8

200

log(3x-4)=-1

x=1.367

300

2ln4x+5=7.773

x=1

400

log_20x+log_20(x+8)=1

x=2

500

log3x-log(x+1)=2.4

No solution, x=-1.102 is extraneous