Mardi Gras Break Number 2
Soooo I’m back again writing my second blog of the break. Once again I will stay I am very bummed that break it over already. I have been super busy all week and it just flew by. I really wanted to aleks extra credit but I did not have any time this week so that sucks. Anyway I’m going to do so more examples from chapter 5 which has to do with like logs and formulas and other stuff. It’s easy enough I guess but I guess we will have to wait for exam grades to be posted to see how well I know my stuff.
Chapter 5 involves three main formulas:
Formula 1 : A(t) = A (1 + r)t
Formula 2: A(t) =A bt/k
Formula 3: P(t) = P er/t
You must choose which formula you use when given a problem.
Example:
You invest 2,000 at 6% intrest compounded continuously. How much money will you have after 3 years?
Plug into your calculator P = 2000e^(.06)(3) = $6371.02
Sunday, March 13, 2011
Mardi Gras Break Blog Number 1
Hey everyone I hope everyone had a great break, I know I did but I am super bummed it’s over already. It seems like it flew by! Anyway the last week we were in school we learned chapter 5 and our exam we took on Friday was on chapter 5. I hope I did okay enough on it to pass (: Now let’s see if I remember how to do any of this stuff cause it’s been awhile…Rational Exponents look easy enough so let’s get started, here ya go!
Exponents that involve roots:
Example 1:
3 square root of 4 = 41/3
Example 2:
(9/25)1/2 = 91/2/251/2 = square root 9/ square root 25 = 3/5
Solve :
Example 3:
49 4x = 78
(72)4x = 78 Bases must be the same
78x = 78
8x = 8 Set exponents equal
X = 1
Okay I think this blog screwed up the way everything looks but your smart people and can figure it out for yourselves.
Hey everyone I hope everyone had a great break, I know I did but I am super bummed it’s over already. It seems like it flew by! Anyway the last week we were in school we learned chapter 5 and our exam we took on Friday was on chapter 5. I hope I did okay enough on it to pass (: Now let’s see if I remember how to do any of this stuff cause it’s been awhile…Rational Exponents look easy enough so let’s get started, here ya go!
Exponents that involve roots:
Example 1:
3 square root of 4 = 41/3
Example 2:
(9/25)1/2 = 91/2/251/2 = square root 9/ square root 25 = 3/5
Solve :
Example 3:
49 4x = 78
(72)4x = 78 Bases must be the same
78x = 78
8x = 8 Set exponents equal
X = 1
Okay I think this blog screwed up the way everything looks but your smart people and can figure it out for yourselves.
Friday, March 11, 2011
mardi gras blog #2
guess what everyone?! rascal flatts concert is sundayyy! which is why im posting early and not waiting last minute :)
i hope everyone had a great mardi gras holiday like i did although i was busy everyday!
FORMULAS:
logb MN=logbM + logbN
logb M/N=logbM - logbN (anything in the bottom is NEGATIVE)
logM^k=KlogM
to set 2 log equal set the insides equal.
**right side is expanded
**left side is condensed
EXPAND:
logbMN^2
logbM+logbN^2
=logbM+2logbN
CONDENSE:
log 45-2log3
log45-log3^2
log45-log9
log45/9
=5
byeeeeee peeps :)
guess what everyone?! rascal flatts concert is sundayyy! which is why im posting early and not waiting last minute :)
i hope everyone had a great mardi gras holiday like i did although i was busy everyday!
FORMULAS:
logb MN=logbM + logbN
logb M/N=logbM - logbN (anything in the bottom is NEGATIVE)
logM^k=KlogM
to set 2 log equal set the insides equal.
**right side is expanded
**left side is condensed
EXPAND:
logbMN^2
logbM+logbN^2
=logbM+2logbN
CONDENSE:
log 45-2log3
log45-log3^2
log45-log9
log45/9
=5
byeeeeee peeps :)
Mardi gras blog #1.
so last week we completed chapter 5 and took our super hard exam. anddddd we did aleks.
chapter 5 was pretty decent, logs are not THATTTTTTT bad but i guess i didnt know them as good as i thought.
writing in exponentials.
EXAMPLE.
log4 64=3
4^3=64.
^^that's your answer. soooooo easy.
there's some with word problems but im not very good at making up word problems much less making them with numbers that will actually give me a normal answer :(
FORMULAS:
a(t)=a0(1+r)^t
a0----your starting point.
r----your decimal number
t----time ( must match rate )
(used with percents)
a(t)=a0 b ^t/k
(used when doubling, halfing, tripling)
p(t)=P0e^rt
p0---starting point
r---rate as decimal
t---time
Keywords (continuously, compounding)
so last week we completed chapter 5 and took our super hard exam. anddddd we did aleks.
chapter 5 was pretty decent, logs are not THATTTTTTT bad but i guess i didnt know them as good as i thought.
writing in exponentials.
EXAMPLE.
log4 64=3
4^3=64.
^^that's your answer. soooooo easy.
there's some with word problems but im not very good at making up word problems much less making them with numbers that will actually give me a normal answer :(
FORMULAS:
a(t)=a0(1+r)^t
a0----your starting point.
r----your decimal number
t----time ( must match rate )
(used with percents)
a(t)=a0 b ^t/k
(used when doubling, halfing, tripling)
p(t)=P0e^rt
p0---starting point
r---rate as decimal
t---time
Keywords (continuously, compounding)
5-6
Mardi Gras Break Blog #2:
5-6
Properties of Logs:
1. Log b MN = log b M + log b N
2. Log b M/N = log b M – log b N
3. Log b M^k = k log b M
(RIGHT SIDE IS CONDENSED, LEFT SIDE IS EXPANDED).
EXAMPLE 1: Condense log M – 3 log N
A). First, check to see which property it’s following. With the – sign, we automatically know the
answer will be in fraction form, property #2.
B). Also, the second half (3 log N) is property #3. Changing that, we get log N^3
C). Now we can continue..
log M/log N^3
EXAMPLE 2: Condense log 8 + log 5 – log 4
A). Simply the 3 parts to get 2 so we can condense. Since log 8 and log 5 are the same, multiply 8 and 5.
B). Now we have log 40 – log 4.
C). Having the – sign, we know we’re going to follow property #2.
log 40/log 4
D). Your answer is 10.
EXAMPLE 3: Expand log b MN^2
A). Following property #1, we get log b M + log b N^2
B). Now bring all exponents to the front to get your final answer.
log b M + 2 log b N
5-6
Properties of Logs:
1. Log b MN = log b M + log b N
2. Log b M/N = log b M – log b N
3. Log b M^k = k log b M
(RIGHT SIDE IS CONDENSED, LEFT SIDE IS EXPANDED).
EXAMPLE 1: Condense log M – 3 log N
A). First, check to see which property it’s following. With the – sign, we automatically know the
answer will be in fraction form, property #2.
B). Also, the second half (3 log N) is property #3. Changing that, we get log N^3
C). Now we can continue..
log M/log N^3
EXAMPLE 2: Condense log 8 + log 5 – log 4
A). Simply the 3 parts to get 2 so we can condense. Since log 8 and log 5 are the same, multiply 8 and 5.
B). Now we have log 40 – log 4.
C). Having the – sign, we know we’re going to follow property #2.
log 40/log 4
D). Your answer is 10.
EXAMPLE 3: Expand log b MN^2
A). Following property #1, we get log b M + log b N^2
B). Now bring all exponents to the front to get your final answer.
log b M + 2 log b N
5-7
Mardi Gras Break Blog #1:
5-7
When solving for a variable as an exponent, you take the log of both sides. Then you bring the exponent to the front and solve.
EXAMPLE 1: Solve 10^x=4
A). Take the log of both the left and right side.
log 10^x = log 4
B). Now, bring the exponent to the front.
x log 10 = log 4
C). Solve for the variable, in this case x.
X = log 4/log 10
EXAMPLE 2: Solve 3^x=81
A). Take the log of both sides.
log 3^x = log 81
B). Bring the exponent to the front.
x log 3 = log 81
C). Solve for x.
x = log 81/log 3
D). Your final answer is 4.
To change a base given log b^a:
log x^a/ log x^b
EXAMPLE 1: Change log 3^7 to base 4.
A). Using the formula, you get
log 4^7/log 4^3
5-7
When solving for a variable as an exponent, you take the log of both sides. Then you bring the exponent to the front and solve.
EXAMPLE 1: Solve 10^x=4
A). Take the log of both the left and right side.
log 10^x = log 4
B). Now, bring the exponent to the front.
x log 10 = log 4
C). Solve for the variable, in this case x.
X = log 4/log 10
EXAMPLE 2: Solve 3^x=81
A). Take the log of both sides.
log 3^x = log 81
B). Bring the exponent to the front.
x log 3 = log 81
C). Solve for x.
x = log 81/log 3
D). Your final answer is 4.
To change a base given log b^a:
log x^a/ log x^b
EXAMPLE 1: Change log 3^7 to base 4.
A). Using the formula, you get
log 4^7/log 4^3
Sunday, March 6, 2011
5-7
Last week we learned section 5-7. In 5-7 it was dealing with log and solves it by a variable as an exponent.
To solve for a variable as a exponent you take the log of both sides, bring the exponents to the front and solve.
- to change a base given log( base is b)^a
Log( base x)^a/log( base x)^b is where x is the base you want
Examples:
Change log (base 5)^8 to base 2
Log(base 2)8/ log (base 2) 5
Solve 3^x=81
Log 3^x=log 81
X log 3= log 81
X=log 81/log 3 = 4
If you know all your steps and the procedure of doing this you will not get stuck on this and it will be really easy for you.
To solve for a variable as a exponent you take the log of both sides, bring the exponents to the front and solve.
- to change a base given log( base is b)^a
Log( base x)^a/log( base x)^b is where x is the base you want
Examples:
Change log (base 5)^8 to base 2
Log(base 2)8/ log (base 2) 5
Solve 3^x=81
Log 3^x=log 81
X log 3= log 81
X=log 81/log 3 = 4
If you know all your steps and the procedure of doing this you will not get stuck on this and it will be really easy for you.
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