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Question 525473: NATURAL LOGARITHMS: ln (1/e)= -1 -----why?
i've looked through my book and it lists the natural logarithms properties but i can't find why ln (1/e)= -1 ... right of the bat, i went "oh, -1", but i can't find a logical step-by-step process to explain why the answer is -1... any help?
Click here to see answer by jim_thompson5910(28717)

Question 525283: Jimmy invests $20,000 in a account that pays 4.24% compounded quarterly. How long( in years and months)will it take for his investment to reach 23,000
Click here to see answer by lwsshak3(6763)

Question 525231: Solve for x:
2 log base 5(7-x)-log base 5 3=log base 5 12
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Question 523632: Solve the exponential equation. Give the exact value for x. (Express all logarithmic functions in terms of ln(x) in your answer.)
text((a) ) e^x = 11
x =
text((b) ) e^x = 2.3
x =
text((c) ) e^x = 36.0
x =
Click here to see answer by lwsshak3(6763)

Question 524181: A robot is projected from the moon with its height in feet given by:
f(x)=-0.0013x^2+1.727x
where x is the time in seconds. Find the maximum height the robot can reach and the time it takes to get there. Round to the nearest tenth.
Click here to see answer by lwsshak3(6763)

Question 521866: given log base 16 of u = 3.7
log base 4 of u^100
how do i go about solving this?
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Question 525629: solve for x
ln x + ln x^2 = 3
Click here to see answer by prateekagrawal(56)

Question 526441: solve for x
log x +log(x-15)=2
Click here to see answer by nerdybill(7009)

Question 526427: write ln(3)-ln(4)+ln(8) as a single logarithm with a coefficient of 1
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Question 526358: Solve for x: log(x+25)=1+log(2x-7)
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Question 526583: 2e^x-2e^-x=5
2e^x-2/e^x=5
let e^x=y.
2y-2/y=5
2y^2-2=5y
2y^2-5y-2=0

Click here to see answer by Alan3354(31534)

Question 526672: How do I solve for the variable
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Question 526775: The sides of a triangle have lengths log(base 2)3, log( base 2)7,and log(base 2) x. Find the least possible integral value of x?

Click here to see answer by KMST(1936)

Question 526762: Can you please help me figure out how to solve this problem?
log(40x+200)=3
Here is what I came up with.
log40x+log200=3
log40x+2.301=3
log40x=.699
x=.4363
When I plug X back into the equation, it doesn't come out right.
Click here to see answer by Earlsdon(6294)

Question 527019: solve for x and express in terms of natural logs:
6^x+2=12^x-1
Click here to see answer by Alan3354(31534)

Question 527083: log[30x^2+x]=0
Click here to see answer by nerdybill(7009)

Question 527085: log base8 [(x+8)(x+9)]=2
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Question 527241: Contract the expressions. That is, use the properties of logarithms to write each expression as a single logarithm with a coefficient of 1.
ln (3) - 2 ln (4) + ln (8)
ln (3) - 2 ln (4+8)
ln *3) - 2 (ln (4) +ln (8)

Click here to see answer by stanbon(57979)

Question 527313: There are (2) questions:
1. Condense the expression to the logarithm of a single quantity: 1/2 ln (2x-1) - 2 ln (x+1)
2. Solve the exponential equation algebraically: 3e^-5x = 132.
Need help answering these two questions someone please help...
Click here to see answer by thinkinbig2(5)

Question 527528: log[2](log[2](log[3](2x-1)))=1
Click here to see answer by nerdybill(7009)

Question 527598: evaluate each of the following
log_x x3 and log_m m
Click here to see answer by stanbon(57979)

Question 527623: I need help with money and compound interest for example principal $8500 rate 7% compounding quartley for 5 years I am not sure how to set up and solve sets, also I am gettin confused with investments like finding the accumulated value of an investment for instance investment of $2000 at 8% compounded semi annually for 9 years
Click here to see answer by rfer(12730)

Question 527838: The percent of U.S. children growing up with out a father has increased rapidly since 1950. If x represents the number of years since 1900 the function is defined by:
F(x)=25/(1+1364.3 e^(-x/9.316) )
What percent of U.S. children lived in a home without a father in 1997

Click here to see answer by stanbon(57979)

Question 527954: 4^x+3=8^x

Click here to see answer by jim_thompson5910(28717)

Question 527917: solve for x- log3(2x-1)=2+log3(x-2)
Click here to see answer by lwsshak3(6763)

Question 527919: log4(x2+3x)=1
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Question 528057: Show that log((4o^log3)/(3^log4))=log3
Click here to see answer by KMST(1936)

Question 528380: log2x+5log2y−3log2z how do you make this a single log?
Click here to see answer by Earlsdon(6294)

Question 528437: please help me with this: log 4.17= 0.6201 find: a. log 417 b. log 0.417 without using calculator
Click here to see answer by scott8148(6628)

Question 528654: 9^x*3^(x2)=81^2
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Question 528566: "graph the function f(x)=4^x. Indicate the y-intercept and the asymptote. Also graph the function g(x)=log_4x. Indicate the x-intercept and the asymptote"
Click here to see answer by lwsshak3(6763)

Question 529226: how do I evaluate this: log2 120 − log2 12 − log2 40
Click here to see answer by josmiceli(9817)

Question 529007: States solve each equation:
(2/3)^x = 9/4
Click here to see answer by lwsshak3(6763)

Question 528521: log x + log y (x-21)=2
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Question 528335: log6(x+9)log6 x=2 check for extraneous solutions
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Question 528298: solve for X: 4^3x+2=16^3x+2
Click here to see answer by lwsshak3(6763)

Question 529426: use log properties to simplify
ln(x^2-4)-ln(x+2)
Click here to see answer by lwsshak3(6763)

Question 529447: How to subtract fractions and How to do the simplest form?
Click here to see answer by KMST(1936)

Question 529650: how does 8x^3=e^18 equal 2x=e^6
Click here to see answer by josmiceli(9817)

Question 529808: 2logbase4x=8
Click here to see answer by swincher4391(726)

Question 530212: what is -5ln(x)+ln(3y)-ln(2z) as a single logarithm?
Click here to see answer by jim_thompson5910(28717)

Question 530282: Find the integer k, k > 2, for, which log (k - 2)! + log(k - 1)! + 2 = 2 log k!.
Click here to see answer by richard1234(5390)

Question 530327: 5 logb x + 6 logb y condense and write the expression as a single logarithm whose coefficient is 1.
Click here to see answer by lwsshak3(6763)

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