Exponential Rules
The function denoted by f(x)=ax
what is an exponential function/ exponential function f with base a?
Write the equation that would be used to love the lograthmic equation
f(x)=logax
f(x)= loga x
af(x) = x
Condense the following, using the properties of logarithms
6log3 u + 6log3 v
log 3 (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
exponential functions and logarithmic function are examples of ...
what are transcendental functions?
the logarithmic function with base 10
what is the 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
The exponential fool that Evaluate
(x3)2
what is the natural base?
the inverse of the function f(x) = ex
what is the natural logarithmic function?
Expand the following using properties of logarithms: log ( t/c3)7
7 log t - 21 log c
What is the value of x if
elnx=e3
elnx = e3
lnx = 3
x = e3
x= 20.086
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))n(t)
A= $5000 (1+ (0.08/365))12(365)
A= $13057.11
Identify they type of function, as shown below
f(x)= ex
what is the natural exponential function?
logaax=x and aloga(x)=x
what are inverse properties?
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)
if logax = logay, then x=y.
what is the one-to-one property?
condense the following using properties of natural logarithms: lnun
what is nlnu?
Is the following a true statement based on the rule for solving exponential equations?
ax=ay if and only if x=y
True statement
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.