Chapter 8 - Logarithms

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-1)(4)=2y

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

400

Convert to Exponential Form:

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

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

or

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

Solving Log Equations with Log Properties

100

Solve for x:

log_3(x-3)=log_3(55)

x=58

200

Solve for x:

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

x=3

300

Solve for x:

2ln(2)+ln(x)=ln(x+12)

x=4

400

Solve for x:

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

x=32

Expanding/Condensing Logarithms

100

Condense the Logarithms:

log_3(2x)-log_3(5y)

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

200

Completely Expand the Logarithm:

log((2x)/y)

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

300

Condense the Logarithms:

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

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

400

Condense the Logarithms:

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

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