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Converting Log and Exponential Form
Solving Log Equations with Properties
Expanding/Condensing Logarithms
Solving Exponential Equations with Logs
100

Convert to Exponential Form:


log_2(8)=x


2^x=8

100

Solve for x:


log_3(x-3)=log_3(55)

x=58

100

Condense the Logarithms:


log_3(2x)-log_3(5y)


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

100

Solve using Logarithms:


6^x=90

x=2.51

200

Convert to Logarithmic Form:


4^y=x


log_4(x)=y


200

Solve for x:


log_5(x+6)=log_5(3x)

x=3

200

Completely Expand the Logarithm:


log((2x)/y)

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

200

Solve Using Logarithms:

3^(7x)=108

x=0.61

300

Convert to Exponential Form:


log_(x-1)(4)=2y

(x-1)^(2y)=4


300

Solve for x:


2log(2)+log(x)=log(x+12)

x=4

300

Condense the Logarithms:


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

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

300

Solve by Converting:


log_4(x)=5

x=1024

400

Convert to Exponential Form:


2log_(3x)(5-z)=4y


(3x)^(2y)=5-z

or

(3x)^(4y)=(5-z)^2

400

Solve for x:


3log(4)-log(x)=log(2)

x=32

400

Condense the Logarithms:

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

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

400

Solve using Logarithms:


10^(7x)=60

x=0.2540216072

500

Convert to Logarithmic Form:


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


log_8(2y-7)=x+4

500

Solve for x:


2log(x)=log(3x+4)

x=4

-1 is an extraneous solution (meaning it won't work)

500

Completely Expand the Logarithm:


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

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

500

Solve using Logarithms:


4^(x-2)=100

x=5.32