Exponential Rules
What type of function is the function shown by f(x)= ax
an exponential function/ exponential function f with base a?
State the type of function show below and the base of the function f(x)=logax
logarithmic function with base a?
Condense the following, using the properties of logarithms
6log3 u + 6log3 v
log3 (u6 v6)
Solve the equation below
log (4k − 5) = log (2k − 1)
log (4k − 5) = log (2k − 1)
4k-5 = 2k -1
4k-2k= -1+5
2k = 4
k = 2
The total gallon of Orange juice each person consumes yearly has decreased 4.1% each year. In 1981 each person drank 16.5 gallons of orange Juice on average. What was the approximate amount consumed in 2010
y = a.bx
y = 16.5 ( 1 - 0.04)29
y = 5.1
5.1 gallons of juice consumed per person
The inverse of the exponential form is ?
the logarithmic form
What is the logarithmic function with base 10 called?
common logarithmic function?
condense the following using properties of logarithms: 2 log 7
3
log (72)1/3
Solve the equation below
3 1 − 2x = 243
3 1 − 2x = 243
3 1 − 2x =35
1 - 2x = 5
1 - 5 = 2x
-4 = 2x
-2 = x
You buy a car for $7500 that depreciated at a rate of 15% a year.
a) How much is the car worth after 4 years?
b) When will the car be worth $2500 or less
y = a.bx
y = $7500(1- 0.15)4
y =$3915. 05
$2500 = $7500 (1 - 0.15)t
log (2500/7500) = T log(0.85)
T = 7 years
What is the name of the exponential rule that solves (x3)2
the power of a power rule or Power rule
What is the name of the inverse of the function f(x) = ex called?
natural logarithmic function?
Expand the following using properties of logarithms: log ( t/c3)7
7 log t - 21 log c
elnx=e3 is calle...
what is exponentiate each side?
Mary invested $5000 into an account that earns 8% interest compounded daily. After 12 years What is the amount in the account?
A= P(1+ r/n)nt
= $5000 ( 1+0.08/365)365*12
=$5000 (1.000219)4380
= $$13057.11
Simplify the following
(24x2y4)3
= 24*3 x2*3 y4*3
= 212 x6 y12
=4096 x6 y12
Solve the following
logaax= and aloga(x)=
a)logaax = x (inverse property)
b) aloga(x) = (inverse property)
condense the following using properties of logarithms: logaun
what is nlogau?
Solve the equation. Round your answers to the nearest ten-thousandth.
6e 5x − 6 − 4 = 50
6e 5x − 6 − 4 = 50
6e 5x − 6= 54
e 5x − 6 = 9
5x - 6= ln(9)
x = (2.1972+6) / 5
x = 1.6394
When Jacob was born $18000 was invested in his trust fund at a rate of 6.25% interest, compounded continuously.
a) What was the balance in Jacob's account at age 15?
b) How old will Jacob be when his investment reaches $75000
A =Pert
A =18000.e 0.0625 (15)
A = $45964. 61
b) $75000 = $18000 .e 0.0625 (t)
ln ($75000/$18000) = 0.0625 t
ln (1.4271) / 0.0625 = t
T = 23 years (approximately)
State and define the laws of exponents
Multiplying exponents - same bases, add exponents
Dividing exponents- same bases subtract exponents
Power of zero - any base with a 0 exponent is equal 1
Negative exponent - reciprocate base and take positive exponent
Power of One - any base with an exponent of 1 is equal to the base itself.
Power of a Power - keep base and multiply exponents.
Simplify the following
log5 (x-1) - log5 (x-1) =2
(x+1) / (x-1) = 52
x+1 = 25x -25
26 =24x
x= 13/12 or x= 1.08
condense the following using properties of natural logarithms: ln (un)
what is nlnu?
ax=ay if and only if x=y
what is one-to-one properties?
A population of 3000 people doubles in size every 10 years. What is the population size after 50 years?
y =a.bx
y = 3000(2)5
y = 96000
96000 people after 50 years.