Logarithms

Converting Log and Exponential Form

100

Convert to Logarithmic Form:

4^y=x

log_4(x)=y

200

Convert to Exponential Form:

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

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

300

Convert to Logarithmic Form:

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

ln(2y-7)=x+4

Solving Using Log Properties

100

Solve for x:

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

x=3

200

Solve for x:

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

x=32

300

Solve for x:

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

x=4

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:

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

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

Solving Exponential Equations

100

Solve by Rewriting as an Exponential Equation:

log_4(x)=5

x=1024

200

Solve By Taking the Log of Both Sides:

3^(7x)=108

x=0.61

300

Solve using By Converting to a Logarithm, then use the change of base formula:

4^(x-2)=100

x=5.32