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

Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)

Question 840358: evaluate log base 2 of 4 - log base 2 of 16
Click here to see answer by LinnW(1048)

Question 840036: The demand for a certain commodity and the price in dollars are related by p= 500 - 10x^1/2 ,where x is the number (in hundreds) of units of the product demanded.Find the price when the demand is 2500. Please help.thank u
Click here to see answer by LinnW(1048)

Question 832505: How do you find the range of y=2^x-1?
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Question 840040: If the lengths of the sides of a cube are tripled,by what factor will the volume change?
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Question 835257: If log a=4 and log b =2 what is the numberical value of
log radical (a/b^3)
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Question 840475: what is log 0.5^(x)-.25+4 and -3e^(2x)+16=5
Click here to see answer by Fombitz(32388)

Question 834118: How do you solve (64^4/3)^-1/2
Click here to see answer by LinnW(1048)

Question 828576: Solve for x:
Log3(1/9)^x=(x+2)

Click here to see answer by LinnW(1048)

Question 840362: Please solve this problem
Log(x-1)^2=log(-5x-1)
Thank you!
Click here to see answer by LinnW(1048)

Question 840033: how do you solve 10 to the 3x-8=2 to the 5-x
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Question 831354: Solve for x.
8400 = 2400(1.08^(x))
*its 1.08 to the x power*
Click here to see answer by LinnW(1048)

Question 840597: How do I solve for t? If A=$5000, P=$1000, r=2.5%, n=2, where A=P(1+r%/n)^(nt)? This is a compound interest problem using logarithm.
Thank you
Click here to see answer by josgarithmetic(39620)

Question 840762: Log16(x+3/x-1)=1/2

Click here to see answer by MathLover1(20850)

Question 840854: find (fg)(3)
f(x)=xsquare -8
g(x)x-9

Click here to see answer by Fombitz(32388)

Question 841176: solve for x: e^4x=110
Click here to see answer by jim_thompson5910(35256)

Question 841200: The value of x in the expression 4^3x=16^x+1
Click here to see answer by Edwin McCravy(20059)

Question 841313: A radioactive substance has a halflife of 120 years. If 200mg of substance was present, how much of the substance remains after 340 years?
Click here to see answer by ewatrrr(24785)

Question 841168: 2x(lnx)^2
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Question 826546: how to solve 10th root of 1.6
Click here to see answer by tommyt3rd(5050)

Question 820137: 5 log subscript 8, 8
Click here to see answer by tommyt3rd(5050)

Question 841984: How to write log w + log v - 3 log z as the logarithmic of a single quantity.
Please this will be very helpful.
Click here to see answer by josmiceli(19441)

Question 842022: Find the vertex, the y intercept, and the x intercept and graph the function
y=x2-2x-8 (it's x squared)
Click here to see answer by Fombitz(32388)

Question 842021: The half-life of carbon-14 is 5730 years. This means that every 5730 years the amount is reduced by 50 percent. Assume there are three milligrams of carbon in a piece of wood. How much carbon-14 will be in the piece of wood 1000 years from now?
Click here to see answer by josgarithmetic(39620)

Question 842045: Use the properties of logarithms to completely expand the expression log5xy^4
Click here to see answer by Fombitz(32388)

Question 842029: I am needing help with Logarithmic Equations. Ex. log 5x = log (2x + 9). Please explain each step to solving this equation. Thanks, Drake
Click here to see answer by Fombitz(32388)

Question 841973: A radioactive substance has a halflife of 120 years. If 200mg of substance was present, how much of the substance remains after 340 years?
Click here to see answer by josgarithmetic(39620)

Question 842056: I am needing help with Logarithmic Equations. Ex. 2log7 -2r =0. Please explain each step to solving this equation. The 7 that is following the log is the base. Thanks, Drake
Click here to see answer by josgarithmetic(39620)

Question 842058: Ex. −10 + log 3(n + 3) = −10. The answer is {-2}. Can you please explain step by step how the answer is -2? Thank you very much, Drake
Click here to see answer by richard1234(7193)

Question 842109: Find the equation of the tangent to the curve y = e^x at the point where it crosses the Y-axis.
I differentiated y = e^x (which is e^x), which gives you your gradient for the tangent..
Subbing in x= 0 into the original equation;
y = e^(0) = 1
Therefore if y=1, x=0 (exponential function)
Sub into the formula:
y-y1 = m(x-x1)
y-1 = e^x(x-0)
y= xe^x + 1
However the answers say y = x+1. Whilst in theory, i completely understand whyh it would be x+1, i can't seem to resolve the question quantatively. Thank you for your help!
Click here to see answer by ewatrrr(24785)

Question 843021: what would be the range of e^-x ..
Click here to see answer by aulii(13)

Question 843262: Please help me solve this equation:
Click here to see answer by richard1234(7193)

Question 843455: 125^2x=.02
Click here to see answer by LinnW(1048)

Question 844355: Given the parent functions f(x) = log10 x and g(x) = 5x − 2, what is f(x) � g(x)?
A) f(x) � g(x) = log10 x5x − 2
B) f(x) � g(x) = log10 (5x − 2)x
C) f(x) � g(x) = 5x log10 x + 2 log10 x
D) f(x) � g(x) = 2 log10 x − 5x log10 x

Click here to see answer by ewatrrr(24785)

Question 844358: Find the equation of the tangent line at x= -3 for the function f(x)=1/x. Use limits.
Click here to see answer by Alan3354(69443)

Question 844373: If f(x) = log3 (x + 1), what is f−1(2)?
A) 1
B) 8
C) 10
D) 27

Click here to see answer by Edwin McCravy(20059)

Question 845417: Suppose that log base 7 3=a, find log base 7 63.
The answer is 2a+1, and I don't know why.
Click here to see answer by Fombitz(32388)

Question 845665: NOTE: when I previewed the question it seemed like the fractional exponents got cut off at the top. In case they can't be seen, the first three are (2/7) and the last two are (7/2).
My teacher wrote her own series of homework problems with the only instructions being "use the One-to-One Property." I tried to find an answer by manipulating the equations (isolating the term being raised to the 'x' power on one side of the equal sign), but I have not been able to find a common base to finish solving the problems.

I simplified the problem to
I then proceeded to solve it as follows, but this method did not seem to be One-to-One:

Any help is greatly appreciated. Thank you!

Click here to see answer by josgarithmetic(39620)

Question 846344: How do you solve for x when : log base81:5 + log base81: (2x-1)= 1/4
Click here to see answer by josgarithmetic(39620)

Question 846887: Log2x+logx=11
Click here to see answer by Fombitz(32388)

Question 846894: 3^x+1=42 solve for x. approximate your answers to two decimal places.
Click here to see answer by Fombitz(32388)

Question 847088: Hi. I need some help with a math problem.
log[x] (x+4) + log[3] (x-2) = 3
I have no idea what to do, as there are different bases, and I don't understand how to change them.
Click here to see answer by richard1234(7193)

Question 847294: Limx>0 cosec^2x/cot^2x

Click here to see answer by Edwin McCravy(20059)

Question 848015: �if [{(25 raised-3power)raised 5power}raised 0power]raised13power=x,then x=?
Click here to see answer by ewatrrr(24785)

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