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

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Question 143923: A salamander scurries 10 inches along a straight path, then stops and rests. After catching its breath, it scurries (1/3) of its previous distance, continuing along its straight path before stopping to rest again. Tne salamander continues this pattern of travel along a straight path, moving (1/3) of the previous distance each time. Which expression will give the total distance the salamander has traveled after n moves?
A. 10 + (1/3)(10) + (1/3)^2(10) + ... + (1/3)^n-1(10)
B. 10 + (1/3)(10) + (1/3)^2(10) + ... + (1/3)^n(10)
C. 10(1/3)^n
D. 10(1/3)^n-1
Click here to see answer by stanbon(75887)

Question 143989: solve for x
log5(4x)=log5 28
2log x+ log3= log48
2^2x+3 = 2^x-5
4^x= 28
Click here to see answer by jim_thompson5910(35256)

Question 143991: A model for the number of people N in a college community who have heard a rumor is given by the equation: where P is the total population of the community and d is the number of days elapsed since the rumor began. If the number of students is 1,000 find the number of days when 500 students would have heard the rumor.
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Question 143992: Solve the equation
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Question 143993: Solve the equation
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Question 143994: Solve the equation
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Question 144334: Solve the equation ln(4x-2)=ln(8x)
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Question 144332: Please help if you can.
Find the Half-Life or Doubling Time for the following:
Q=1000e^0.5t
I have no idea where to go with this one. Thank you for any help you can offer.
Click here to see answer by scott8148(6628)

Question 144349: The Mach number, M, is the ration of the speed of an object, v, traveling through a fluid medium to the velocity of sound Vs, through that medium. Hence, log(M) =
a. log(v) - log(Vs)
b. log(v-Vs)
c. log(v) + log(Vs)
d. log(v) log(Vs)
Click here to see answer by stanbon(75887)

Question 144348: Determine x for 10^(2x+1) = 100^x
a. x = -1
b. x = 2
c. x = 0
d. No solution
After working a, b, c....I picked answer d.
Click here to see answer by stanbon(75887)

Question 144339: Solve the equation 3^x+1=27^x+3
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Question 144343: Write an exponential function y=ab^x whose graph passes through the given points: (2,16), (3,64)
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Question 144341: Write the exponential function y=ab^x whose graph passes through the given points: (1,6), (2,36)
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Question 144342: Write an exponential function y=ab^x whose graph passes through the given points: (2,16), (3,64)
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Question 144344: Write a power function y=ax^b whose graph passes through the given points: A) (2,2)(4,16) B.) (3,3),(6,12)
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Question 144401: In(x+2)=2
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Question 144403: In(5-x)=6
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Question 144402: In(2x-3)=1.7
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Question 144576: Could someone please help me simplify 1n e^4x-5 thank you
Click here to see answer by Alan3354(69443)

Question 144672: Pls help me for this question : 2^x 3^x+1 = 100 Thanks
Click here to see answer by vleith(2983)

Question 145111: how to evaluate 8^(1/3) without calculator or 8^(2/4)?
Click here to see answer by shahid(44)

Question 145339: which logarithmic equation is equivalent to the exponential equation below?
8^x=100
a. x=log8 100
b. x=log100 8
c. 100=logx 8
b. 8=logx 100
Click here to see answer by jim_thompson5910(35256)

Question 145504: How do you Plot the graphs of the following functions

1. (x)=6x
2. f(x)=3x - 2
3. f(x)=(1/2)x
4. f(x)= log2x

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Question 145459: log3 fifth root of 9
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Question 145806: ln(x-3)=ln(x)+3
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Question 145981: (2/3x^4)(3x^2-9)
Click here to see answer by ankor@dixie-net.com(22740)

Question 146259: Solve the equation by expressing each side as a power of the same base and then equating exponents
e^(x+5)=1/e^6
Click here to see answer by stanbon(75887)

Question 146462: Can someone please help me with this problem: "Write an equivalent exponential expression for 16^2x with a base of 2." Thank you!
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Question 146515: Sorry about the other ?, that was an incomplete eqaution.
(4xy)(5x)
Click here to see answer by checkley77(12844)

Question 146979: The x-intercept of F(x) = log0.5 x is
this isn't out of a textbook.

Click here to see answer by nabla(475)

Question 146747: Find algebraic solutions for each system of equation
b) y= 2(1/3)^(-x) and y=6(9)^(x+1)
c) y= 1000(0.1)^(2x) and y=10^x

thank you!
Click here to see answer by nabla(475)

Question 146991: solve the following equation for x: 64=2^3x.
a.x=1
b.x=2
c.x=2.5
d.x=3
Click here to see answer by oscargut(2103)

Question 146990: solve the following equation for x: 64=2^3x.
a.x=1
b.x=2
c.x=2.5
d.x=3
Click here to see answer by Fombitz(32388)

Question 147371: solve (x+10)(x-4)(x+6)>0
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Question 147557: How do you write log40=1.6 in exponential form and how can you change it to a logarithmic form?
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Question 147642: Find the domain of g(x)=5e^x

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Question 147641: Find the domain of f(t)=log(t-5)

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Question 147718: Can you help me with this please?
What is the difference between #1 and #2 below?
#1 --> Log(A * B)
#2 --> Log(A) * Log(B)
also...
compare:
#1 - Log2(2 * 8)
vs.
#2 - Log2(2)*Log2(8)
Are the values different? Why?
Can you show me another example?
Thank you
Click here to see answer by mangopeeler07(462)

Question 147771: ln(x+2)+ln3=ln39
Click here to see answer by stanbon(75887)

Question 147517: Evaluate 1000(1.025)^-6. Round your answer to three decimal places.
I have done this f(x)=3^x
x y
0 3^0 =1
1 3^1 =3
2 3^2 =9
Thanks
Click here to see answer by Alan3354(69443)

Question 147786: Find the domain of g(t)=5^t? Is the answer t is the set of all real numbers?
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Question 147784: Find the domain of g(x)=ln(x+4)? I am not sure what to do for this question with the ln? Help?
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Question 147790: g(x)=e^x+3
Description of transformation: Equation(s) from Horizontal Asymptote(s): y-intercept in (x,y) form:
I am not sure what this is asking me to do? Help

Click here to see answer by Fombitz(32388)

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