Converting Log and Exponential Form
Convert to Exponential Form:
log_2(8)=x
2^x=8
Solve for x:
log_3(x-3)=log_3(55)
x=58
Condense the Logarithms:
log_3(2x)-log_3(5y)
log_3((2x)/(5y))
Solve using Logarithms:
6^x=90
x=2.51
State the Transformations:
2log(x-3)
2: Vertical Stretch by 2
x-3: Right 3
Convert to Logarithmic Form:
4^y=x
log_4(x)=y
Solve for x:
log_5(x+6)=log_5(3x)
x=3
Completely Expand the Logarithm:
log((2x)/y)
log(2)+log(x)-log(y)
Solve Using Logarithms:
3^(7x)=108
x=0.61
State the transformations:
-ln(x-4)+1
-: reflection over the x-axis
x-4: right 4
+1: up 1
Convert to Exponential Form:
log_(x-1)(4)=2y
(x-1)^(2y)=4
Solve for x:
2ln(2)+ln(x)=ln(x+12)
x=4
Condense the Logarithms:
2ln(3)-2ln(x)+4ln(y)
ln((9y^4)/x^2)
Solve by Converting:
log_4(x)=5
x=1024
What are the four parent points for the logarithm?
log_3(x)
(1/3,-1)
(1,0)
(3,1)
(9,2)
Convert to Exponential Form:
2log_(3x)(5-z)=4y
(3x)^(2y)=5-z
or
(3x)^(4y)=(5-z)^2
Solve for x:
3log(4)-log(x)=log(2)
x=32
Condense the Logarithms:
3log(x)-4log(2)-5log(z)+3log(3)
log((27x^3)/(16z^5))
Solve using Logarithms:
e^(7x)=60
x=0.58
What are the transformed points of the logarithm?
log_3(x)-4
(1/3,-5)
(1,-4)
(3,-3)
(9,-2)
Convert to Logarithmic Form:
e^(x+4)=2y-7
ln(2y-7)=x+4
Solve for x:
2log(x)=log(3x+4)
x=4
-1 is an extraneous solution
Completely Expand the Logarithm:
ln((3x^6y^7)/(7z^5))
ln(3)+6ln(x)+7ln(y)-ln(7)-5ln(z)
Solve using Logarithms:
4^(x-2)=100
x=5.32
What are the transformed points of the logarithm?
log_3(x-2)-1
(2 1/3, -2)
(3,-1)
(5,0)
(11,1)