Jeopardy - Review Exp / Logs

Rational

100

8 = x^(3/2)

x=4

200

9=(x+1)^(1/2)

x=80

300

20=4+(2^x)

x=4

400

16^(3/4)

8

500

Solve: x^(4/3) = 81

x =27

Logs - no calculator

100

Evaluate

log_3(9)= 

2

200

Evaluate

log_4 (8) = 

x = 2/3 

since: 2^(2x)= 2^3

300

2 log x + log3 = log 75

x = 5

since

3x^2 = 75

x^2 = 25

400

Solve:

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

x = 4

(2x)/(x-2) = 4

2x = 4(x-2)

500

Solve for x

log_2(2x)+log_2(5)= 3

x = 4/5 (or 8/10) since

log_2(10x)=3

10x=2^3

Log - with Calc

100

Simplify

log_3(10)

x = 2.096

200

Solve for x

e^x=4

x = 1.306

300

Solve for x

10+3^x = 16

x = 1.631

400

Solve for x

5^(x-8)=45

x = 10.365

500

Solve:  (Extra Credit Level!)

3^(4x+1)=8^(x-5)

x = -4.966
Negative answer is okay since it was not originally a log

Equations

100

Solve for x

4^x*(1/4)^3=16

5

200

Solve:

5^(x-1)*5^(3x+2)=5^(7x+16)

-5

300

write the following expanded form into an expression:

(1/12)^(4x+3)*12^(2x)=12^(2x+9)

-3

400

write the following as an expression:

(1/9)^(2x)*3^(x+5)=81^(x+3)

-1

500

solve:

(1/16)^(x+7)*64^(x+5)=(1/32)^4

-11

Rad or Rat Exp

100

simplify / write without an exponent:

81^(-1/2)

1/9

200

simplify / write without an exponent:

(1/64)^(2/3)

1/16

300

write the following in exponential form and simplify:

∜(16)^2

16^(2/4)

16^(1/2)

4

400

Solve:

4∛(x-1) = 20

126

500

Solve:

√(4x-14) = √(-4-x)

NO REAL SOLUTION!!

(x = -2 does not check, it is extraneous!)