Algebra 2

How do I solve these inequalities:

e^3x>e^x-1

-6log (subscript of 4) x > -24

& how do I solve these:

8^x+1=3

e^x+2=50

8logx=16

I really don't understand how to solve these so can someone please explain them to me?

  1. 👍 0
  2. 👎 0
  3. 👁 499
  1. e^3x>e^x-1

    you probably meant:
    e^(3x) > e^(x-1), (huge difference from what you typed)
    ln both sides
    ln (e^(3x)) > ln e^(x-1)
    3x > x-1
    2x > -1
    x > -1/2

    PROOF:
    http://www.wolframalpha.com/input/?i=plot+y+%3D+e%5E%283x%29+%2C+y+%3D+e%5E%28x-1%29+from+-1+to+0

    -6log (subscript of 4) x > -24
    divide both sides by -6
    log4 x < 4
    x < 4
    but remember we can only take logs of positive numbers, so
    0 < x < 4 , also remember that log(a number between 0 and 1 is negative, and multiplying it by -6 would make the result positive.

    so 1 < x < 256

    check: notice the graph of y = log4 x
    is below y = 4 from 1 to 256

    http://www.wolframalpha.com/input/?i=plot+y+%3D+4+%2C+y+%3D+log%28x%29%2Flog%284%29+from+.1+to+300

    Now for the equations:
    8^x+1=3
    the way you typed it ...
    8^x = 2
    x = 1/3 , since the cuberoot of 8 is 2

    the way you typed it:
    e^x+2=50
    e^x = 48
    ln both sides
    ln (e^x) = ln 48
    x lne = ln 48
    x = ln 48 , since lne = 1

    8logx=16
    divide both sides by 8
    log x = 2
    which means:
    10^2 = x
    x = 100

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra 2

    I'm working on Lesson 6: Absolute Value Equations and Inequalities Algebra 2 A Unit 2: Expressions, Equations, and Inequalities and feel confident in my first few answers, but beyond that am lost. May I have some help? **=the

  2. physics

    I really need help on D part of the following problem: A clever engineer designs a "sprong" that obeys the force law F subscript e = -q(x - x subscript e)^3, where x subscript e is the equilibrium position of the end of the sprong

  3. Math 7 A

    lesson 10: solving inequalities by adding and subtracting Math 7 A Unit 5: Equations and Inequalities, 1. What is -m 7 (less than sign) 6 either A: m Less than -13 B: m Less than 1 C: m Less than -1 D: m less than 13 I think its C

  4. Math

    Solve the compound inequalities. Write the solutions in interval notation. Graph your solution on a number line. 1. 2(3x + 1)< -10 or 3(2x - 4) ¡Ý 0 The or means union of these inequalities. 2. 5(p + 3) + 4 > p - 1 or 4(p - 1) +

  1. Chemistry

    Which element has no stable isotopes? 1. (subscript)27 Co 2. (subscript)51 Sb 3. (subscript)90 Th 4. (subscript)82 Pb I believe it's either 2 or 3, but I can't decide which. I'm not sure how to go about answering this question,

  2. physics

    An ice sled powered by a rocket engine starts from rest on a large frozen lake and accelerates at +13.0 m/s^2. At t(subscript 1), the rocket engine is shut down and the sled moves with a constant velocity v until t(subscript 2).

  3. Algebra 1

    How many solution sets do systems of linear inequalities have? Do solutions to systems of linear inequalities need to satisfy both inequalities? In what case might they not?

  4. Math

    Assume that x,y and a are positive numbers. Use the properties of logarithms to write the following expression - log a x^6 y^7 a. 42log a x+y b. 42log a x+7log a y c. 6log a x+42log a y d. 6log a x+7log a y e. 6log a x+6log a y

  1. Algebra2

    Solve the inequalities by graphing y3x-1

  2. math

    Find the value of each of the following. Leave your answers as fractions where appropriate. Do not change bases. a) log4 (1/8) B)10^(-10log3)

  3. Chemistry

    Three double bonds in Cyclohexene (CH subscript 3) 3 (another subscript) CCl with AlCl (subscript 3) as a catalyst results in what? Then, that added with HNo (subscript 3) and sulfuric acid as a catalyst becomes one minor and one

  4. Math-log

    Solve for X in (Log X)-6Log X+9=0 ³ ³

You can view more similar questions or ask a new question.