Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

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Question 393198: An exponetional function of the form f(x)=a times 2 to the x power passes through the point (3, 24 ) What is the function ?
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Question 393211: If f(0)=2 and f(x+1)=3 times f(x)-5 what is f(4) ?
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Question 393281: 1. 5+2logx=4
2. log(x-2)+log(2x-3)=2logx
3. 4^x+3=7^x
4. log2x + log2 (x+2)=log2 (x+6)
5. 5^(x/2)=123

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Question 393281: 1. 5+2logx=4
2. log(x-2)+log(2x-3)=2logx
3. 4^x+3=7^x
4. log2x + log2 (x+2)=log2 (x+6)
5. 5^(x/2)=123

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Question 393326: evaluate 1/32 to the negative 3/5 power.
I think you have to find out what the cube root of 32 is so you can find ou the cube root of 1/32, and that will cancel out the threes and you get 1/(cube root of 32) to the negitive 1/5, but 32 doesn't have a cube root, and after that I'm just lost. I don't get this at all.

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Question 393342: in the year 2001, the United States will host the international mathematical olimpiad. Let I,M, and O be distinct positive intergers such that the probuct I*M*O=2001. What is the largest possible value of the sum I+M+O?
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Question 393385: Exoponential Method
1.A biologist is researching a newly-discovered species of bacteria. at time t=0 hours, he puts one hundred bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Find an exponential equation thet approximates the information.
2. A $1,000 deposit is made at a bank that pays 12% compound monthly. How much will you havein your account at the end of 10 years.

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Question 393554: e^x=30
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Question 393553: e^x=30
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Question 393681: 1)
3√30x^15/120x^17y^-1
It is a cube root.
2)3√4√10=100^2x
There's 10 inside of cube root and 4th root.
3)9√(2xy^4)^-12/(8x^12y)^2
It is a 9th root.


Thank you so much!!!!!! I have a test on Friday and my teacher really can't teach :(

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Question 393466: hello the question is
1/125=25^2x-1
FIND X:

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Question 393878: What is (3/5) to the 4th power
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Question 393990: If the diameter of a circle is 1.3 x 10^-12 (raised to the -12 power) meters, then what is its radius?
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Question 394055: Evaluate log9 9 exponent of 3
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Question 394053: Write log8 4096=4 in exponent form
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Question 394054: Find antiln 5.3671. Round your answer to three decimal places.
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Question 394126: 3ln(2x^2)=12
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Question 394125: 1+lnx^4=9
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Question 394537: How would you solve 5^(x+1) = 25^(3x)?
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Question 395072: The half life of thorium-229 is 7340 yrs. how long will it take a sampleof this substance to decay to 20% of its original amount?
That is the problem. I need help finding the solution. I know I will use the model A=Aoe^kt. I believe it would go something like:
A/2=Ao/2 ^kt
0.2=???
I need to find my K before I can go further, but I am not sure how to do that. I would appreciate any help! Thank you!!

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Question 395078: Here is the problem I am working on:
A bird species in danger of extinction has a population that is decreasing exponentially. Five years ago the population was at 1400 and today only 1000. Once the population drops below 100, the situation will be irreversible. When will this happen?
I will use the model A=Aoe^kt
I would appreciate any help! Thank You!

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Question 395205: (8^2)^(1/3)
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Question 395520: use the given x-values to graph each function,then graph its inverse. describe the domain and range of each functions
14. f(x)=5^2 ; x= -2,-1,0,1,1.5

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Question 395528: use the given x-values to graph each function,then graph its inverse. describe the domain and range of each functions
15. f(x)= 0.5^x ; x= -2,-1,0,1,2

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Question 395785: How do you solve (1/16) when its squared and rewrite it without exponents
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Question 396163: 81=27x
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Question 396286: 100^x=10
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Question 396352: I need help with this Logarithmic problem in a simple to understand way, thank you. 4-2e^x=-23
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Question 396452: Write e3 = x in logarithmic form. The number 3 in this problem is an exponent.
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Question 396570: Find the domain of
a)(√x-2)-log(5)(10-x)
b)Inx + In(2-x)

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Question 396671: y=3/5*3^x
match the functin rule with the graph of the function

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Question 396672: supose an investment of 4,500 doubles in value every ten years how much is the investment worth after 50 years?
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Question 397023: simplify expression 25√2*125√2
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Question 397032: How do you solve for x in: 2lne^x+lne^3x=4
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Question 397118: Logb7=13 or log( b, 7 )=13

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Question 397152: how do you evaluate the logarithm 3 log(base2)of2 - log(base2)of4?
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Question 397770: Question:
Find the area bounded by 1-e^(-2x) in the interval x = -1 to x = 1.
Thank-you in advance.

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Question 398220: Ive totally lost myself with this, so if there is anyone that can help please

2log[4](x)+log[4](3)=log[4](x)-log[4](2)

All the 4s are log base 4
Thank you

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Question 398285: I took a pre -test and missed a couple im not sure how to do if it all possible
work them out with explanations of why it was done that way so it well help me understand.
Solve. What is the largest solution log[x+3]4=2
thex+3 will be base of the log
2log[4]x+log[4]3=log[4]x-log[4]2
all the 4 s are the baseof the log
solve 3^(x+1)=7^(x-4) round your answerto the nearest hundredth
Thank you

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Question 398428: Give the domain of F(x)=2x^2+3x-5
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Question 398624: I need step by step explanations for problems like log%28b%29%28x%5E2-15%29=log%28b%29%286x%2B1%29
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Question 398519: Milk costs $2.74 in 2002 if the rate of inflation continues it would cost $3.41 in 2024. What is the rate of inflation in July 2002?
All I have so far to find out the equaiton is-
y=y1(b)^x-x1
3.41=2.74(b)^22 but I'm not sure if this is correct or the right way to figure it out

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Question 398983: (1/16)^x+1=(1/8)^2x-1
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Question 398985: evaluate these expressions
log(1/3)27
Log(8) 4

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