Converting
Convert to Logarithm Form
15^x=730
log_15(730)=x
What is the Range for ALL Logarithm functions?
(-oo, oo)
ARN
Shifted 3 units up and 5 units shifted to the left.
y=log(x+5)+3 or
y=log10(x+5)+3
logx9=2
x=3
What is the inverse equation of logb(x)=y?
bx=y
True or False: The value of logb x is positive
False: range is all real numbers
Evaluate the following expression
log8(8)=
1
f(x)=log_2x
f^-1(x)=2^x
How old is Ms. Mendoza
31 (as of jan 2024)
Convert to Logarithm Form
x4=625
logx(625)=4
What is the Domain of:
f(x)=log_2(x)
x>0
(0, oo)
Shifted 2 units to the right & 5 units down
y=log(x-2)-5 or
y=log10(x-2)-5
log2(x)=3
8
For logb(x)=y , Why must the inputs be x>0 ?
Because of the asymptote, x=0, restricts our domain options.
True or False: logbx is not a valid expression if x is a negative number.
True because of our domain restrictions, x>0.
Evaluate the following expression
log5(5-4)=
-4
f(x)=log_2x -1
f^-1(x)=2^x +1
How many siblings does Ms. Mendoza have?
2 brothers
Convert to Exponential Form
log_b(m)=w
b^w=m
What is the Domain of:
f(x)=2log(x+3)-5
(-3, oo)
x> -3
Shifted 7 units up & 1 unit the left with a vertical stretch of 3.
y=3log(x+1)+7 or
y=3log10(x+1)+7
Solve for x:
log2(x)=-1
1/2 or .5
logbx=y
What happens to a log graph when 0<b<1 ?
The function is reflected across the x-axis
True or False: logb1=0 for any base, b>0.
True: b0=1 for b>0
Evaluate the following expression
log4(1)=
0
f(x)=log_2(x+3)
f^-1(x)=2^x -3
How long has Ms. Mendoza been teaching at PHS?
This will be my 3rd year.
Convert to Exponential Form
Log_(2b)(XY)=37
(2b)^37=XY
What is Domain of:
f(x)=log_2(x-1)-4
x> 1
Shifted 3 units to the right, shifted 11 units up, & reflected across the x-axis.
y= -log(x-3)+11 or
y= -log10(x-3)+11
log6(4x-8)=2
x=11
logbx=y
What values of b, DO NOT make sense? AKA for what values of b is y=logbx not defined?
b=0 and b=1 b negative
(in rare occasions, the graph would be discrete)
True or False: logb(b)=1 for any b>0.
True because b1=b
Evaluate the following expression
log3(1/9)=
-2
f(x)=log_4(x+3)-2
f^-1(x)=4^(x+2) -3
What is Ms. Mendoza's favorite food?
tacos
(bonus if you choose carnitas tacos)
Convert to Logarithm Form
3^(2x+1)=F
Log_3(F)=2x+1
What is Domain of:
f(x)=log_3(x+5)-4
x> -5
Reflected across the x-axis, shifted down 3 units, shifted to the left 6 units, and vertically compressed 1/2.
y= -1/2 log(x+6)-3 or
y= -1/2 log10(x+6)-3
log16(64)=x
x=3/2
That is the inverse function of log8(x-1)=y
y=8x+1
True or False: log4(x) < log6(x) for any value of x.
False log4(x) = log6(x) when x=1
Evaluate the following expression
log8(16)=
4/3
f(x)=log_3(x-5)+6
f^-1(x)=3^(x-6) +5
Spain