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 436457: Simplify the logarithm
log 4 root 2
Click here to see answer by robertb(4012)

Question 436460: Simplify the logarithm
log1/9 4 root 3
Click here to see answer by robertb(4012)

Question 436538: Given that loga(2)=0.301, and loga(3)=0.477, find loga(6)
A) Can't be found from given info.
B) 0.091
C) 0.144
D) 0.778
E) None of the above
Click here to see answer by stanbon(57984)

Question 436572: solve for x
10^x-1 = e^x+1
the raised expression is x-1 for 10
the raised expression is x+1 for e
Click here to see answer by Alan3354(31538)

Question 436571: solve for x
m = a(over)1+be^x
Click here to see answer by stanbon(57984)

Question 436570: Combine
3log(base2)x + 1(over)2log(base8)x - 2log(base2)(x+1)
1(over)2 is a fraction like one-half
Click here to see answer by stanbon(57984)

Question 436617: Im not sure if this is the right section, but if anyone can help me with the following types of problems I would greatly appreciate. I just realized I have the wrong text, and there are no examples!! Thank you!
Find the following limit:
lim
x -> 3
2x^2-9x+2

Find the following limit:
lim
x -> 2
2x-1/3x+4
The equation part should be directly across from the lim, however this application makes that impossible. Thanks!!
Click here to see answer by richard1234(5390)

Question 436769: find the difference quotient of x^3+ 3x^2-4x+5
Click here to see answer by robertb(4012)

Question 436863: Find the future value of an initial investment of $5,000 invested at 7% compounded annually, for 25 years.
the formula is: FV=PV(1+i)^n when
FVn is the Futer value of the investment after n years
Pv is the initial amount of the investment
i is the interest rate.
n is the length of the investment, in years.
I have set the equation up like this
FVn= 5,000(1+7%)^25
FVn=5,000(1+0.07)^25
FVn=5,000(1.07)^25
Is this the correct set up?
Now I know since I have the 25 exponent, I have to multiply the 1.07 times itself 25 times, can someone help me from that step. I do not have a scientific calculator so I really need assistance with the multiplication of the exponent and the solution to the problem.
thank you in advance for your assistance
Click here to see answer by stanbon(57984)

Question 436896: How would I solve this problem?
Graph the equations of the system. Then solve the system to find the points of intersection.
y = x to the power of 2 - 6x + 9
y = -x + 3
Do I need to find the intersections first before I can graph?
Thank you very much for your help.
Click here to see answer by MathLover1(6815)

Question 437367: combine
2log(base5)x - 2log(base5)(x+1) + log(base5)x
Click here to see answer by ewatrrr(10682)

Question 437368: solve for x
3log(base10)x+log(base10)x^2=2
Click here to see answer by ewatrrr(10682)

Question 437371: expand
log(base9)7(over)8y
Click here to see answer by ewatrrr(10682)

Question 437370: expand
log(base4)x^2+5(over)x^3
Click here to see answer by ewatrrr(10682)

Question 437369: expand
log(base2)3(x^2+y)(over)z
numerator is 3(x^2+y)
demoninator is z
Click here to see answer by ewatrrr(10682)

Question 437403: g(x)=(x+2)^2
____________
x^2+5x+6
Click here to see answer by ewatrrr(10682)

Question 437404: Please help:
e^(x^2+7x)/(1/e^12)
Click here to see answer by stanbon(57984)

Question 437414: Sorry should have been an equal sign
e^(x^2+7x)=(1/e^12)

Click here to see answer by stanbon(57984)

Question 437419: 6^=x
Click here to see answer by edjones(7569)

Question 437539: Use the approximate doubling time formula (rule of 70) for the case described below. Discuss whether the formula is valid for the case described:
An economic indicator is increasing at the rate of 7% per year. What is the doubling time? By what factor will the indicator increase in 3 years?
Thank you.
Click here to see answer by stanbon(57984)

Question 437638: Verify that the two function are inverse functions algebraically:
f(x)=4x+9 g(x)=x-9/4
Click here to see answer by richard1234(5390)

Question 437775: how do i graph this? please help
log2(x+3)+1
Click here to see answer by MathLover1(6815)

Question 437825: Combine
4log(base5)x - log(base5)x + log(base5)(x+2)
Click here to see answer by Gogonati(817)

Question 437891: solve for x
log(base5)(x+3) - log(base5)x = 2
Click here to see answer by ewatrrr(10682)

Question 437888: solve for x
log(base4)(x^2-3x) = 1
Click here to see answer by josmiceli(9819)

Question 437892: combine
2log(base8)x - 2/3log(base8)x + 4log(base8)
not sure how to combine with the fraction.
Click here to see answer by ewatrrr(10682)

Question 437822: Combine
2log(base8)x - 2(over)3log(base8)x + 4log(base8)x
2(over)3 is a fraction as in two-thirds
Click here to see answer by ewatrrr(10682)

Question 437896: log8 x^2 = (log8 x)^2
Click here to see answer by josmiceli(9819)

Question 438096: I am trying to do logarithmic equations and is having a difficult time finding a solution. Please help.
The problems are:
Problem #1: log(base3)x = 2 log(base3)3 + log (base3)5
Problem #2: log(base5)(x^2-9) = 4
Click here to see answer by lwsshak3(6770)

Question 438117: evaluate: log5 125. 5 is the base
Click here to see answer by Alan3354(31538)

Question 438646: 2log x - 2log(x^2+1) +3log(x-1) as a single logarithm? Thank you so much for your help
Click here to see answer by stanbon(57984)

Question 438992: (4/3)^1-x =5^x

Please show me how to solve this showing all steps. I tried taking the ln of both sides and ended up with x=.47, which is wrong. I know the answer is x=0.15, but am not sure how to get there. Below I will show my original work done so you can see that I have tried, even though I am certain it is incorrect.
(4/3)^1-x=5^x
(1-x) ln4/3=x ln5
ln4/3-(ln4/3)x=(ln5)x
x= ln4/3 =.47
___________
ln5 + ln4/3
Click here to see answer by stanbon(57984)

Question 439029: please help me solve these equations: ln(4x)=3 and 4+5e^(-x)=0
Click here to see answer by stanbon(57984)

Question 439529: F(t) = P(1 + r/n)nt Need the future value of an investment as an exponential function with time as the independent variable. F(t) = P(1 + r/n)nt. If P= 25000 (Investment), r = 6% (Interest Rate), t = 18 (yrs), n= 2 (Compounded SemiAnnual). What is the future value of the investment?

Click here to see answer by Gogonati(817)

Question 439583: Expand the logarithm
logx^2 y^3
Click here to see answer by John10(267)

Question 439693: Please help me understand how 4e^0.036(14) resulted to 6.62. Thank you.
Click here to see answer by lwsshak3(6770)

Question 439905: The population of a certain country grows exponentially so that its doubling time is 42 years. If the present population is 12.5 million, what will the population be in 126 years?
Click here to see answer by stanbon(57984)

Question 440001: The problem is log 4 [log 3(x)]= 1

What value of x makes this true?
Click here to see answer by stanbon(57984)

Question 439961: write the following equation as a logarithmic equation.
2^-4 = 1/16
Click here to see answer by robertb(4012)

Question 441074: log₇12=log₇(4x-6)
Click here to see answer by stanbon(57984)

Question 441079: log₇(x^2+x)=log₇56
Im supposed to solve. but I don't know where to begin.
Click here to see answer by stanbon(57984)

Question 441079: log₇(x^2+x)=log₇56
Im supposed to solve. but I don't know where to begin.
Click here to see answer by nerdybill(7011)

Question 441067: 1. how long does it take 1700 to double if it invested at 5% interest , compound monthly?
2. what annual rate of interest is required to doulbe an investment in 7 years?
Click here to see answer by lwsshak3(6770)

Question 441044: i need help solving 2x^3+2x^2-19x+20=0
Click here to see answer by lwsshak3(6770)

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