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Converting Log and Exponential Form
Solving Algebraic Log Equations
Expanding/Condensing Logarithms
Rational Expressions
Rational Equations
100

Convert to exponential form:


log_2(8)=x


2^x=8

100

Solve for x. Round to the nearest hundredth.


5^(2x)=21

x=0.95

100

Condense:


log_3(2x)-log_3(5y)


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

100

Simplify:

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


(x-4)(x-2)

100

Solve for x:

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

x=14

200

Convert to logarithmic form:


4^y=x


log_4(x)=y


200

Solve for x. Round to the nearest hundredth.


5*2^x=240

x=5.58

200

Completely expand:


log((2x)/y)

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

200

Simplify:

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

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

200

Solve for x:

x+5/x=-6

x=-1, -5

300

Convert to exponential form:


log_(x)(4)=2y

(x)^(2y)=4


300

Solve for x:


3^(2x)=27

x=1.5

300

Condense:


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

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

300

Simplify:

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

x+y

300

Solve for x:

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

x=-23

400

Convert to exponential form:


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


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

400

Solve for x. Round to the nearest hundredth.


2*3^(x-5)=12

x=6.63

400

Condense:


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

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

400

Simplify:

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

(x^2+1)/x

400

Solve for x:

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

No solution!

500

Convert to logarithmic form:


2^(x+4)=y


log_2(y)=x+4

500

Solve for x. Round to the nearest hundredth.


 2^(3x)-7=13

 x=1.44

500

Completely expand:


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

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

500

Simplify:

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


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

500

Solve for x:

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

x=-17, 3