IM3 Logs & Rational Expressions/Equations Review

Converting Log and Exponential Form

100

Convert to exponential form:

log_2(8)=x

2^x=8

200

Convert to logarithmic form:

4^y=x

log_4(x)=y

300

Convert to exponential form:

log_(x)(4)=2y

(x)^(2y)=4

400

Convert to exponential form:

log_(3)(5-z)=4y

(3)^(4y)=5-z

500

Convert to logarithmic form:

2^(x+4)=y

log_2(y)=x+4

Solving Algebraic Log Equations

100

Solve for x. Round to the nearest hundredth.

5^(2x)=21

x=0.95

200

Solve for x. Round to the nearest hundredth.

5*2^x=240

x=5.58

300

Solve for x:

3^(2x)=27

x=1.5

400

Solve for x. Round to the nearest hundredth.

2*3^(x-5)=12

x=6.63

500

Solve for x. Round to the nearest hundredth.

 2^(3x)-7=13

 x=1.44

Expanding/Condensing Logarithms

100

Condense:

log_3(2x)-log_3(5y)

log_3((2x)/(5y))

200

Completely expand:

log((2x)/y)

log(2)+log(x)-log(y)

300

Condense:

2log(3)-2log(x)+4log(y)

log((9y^4)/x^2)

400

Condense:

3log(x)+4log(2)-5log(z)-3log(3)

log((16x^3)/(27z^5))

500

Completely expand:

log_7((3x^6y^7)/(z^5))

log_7(3)+6log_7(x)+7log_7(y)-5log_7(z)

Rational Expressions

100

Simplify:

(x^2-16)/(x-3)*(x^2-5x+6)/(x+4)

(x-4)(x-2)

200

Simplify:

(2x)/(x^2-4)+(3)/(x+2)

(5x-6)/((x+2)(x-2))

300

Simplify:

x^2/(x-y)+y^2/(y-x)

x+y

400

Simplify:

(1/x^3-x)/(1/x^2-1

(x^2+1)/x

500

Simplify:

(1/3+2/x)/(1+x/3)

(x+6)/(x(x+3))

Rational Equations

100

Solve for x:

(x-5)/(x+1)=3/5

x=14

200

Solve for x:

x+5/x=-6

x=-1, -5

300

Solve for x:

50/x-50/(x-2)=4/x

x=-23

400

Solve for x:

1/(2x)-2/(5x)=1/(10x)-3

No solution!

500

Solve for x:

(9x-45)/(x^2+6x)=1/x-1

x=-17, 3