# 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

## 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