Question

Please lord help, I have a test tomorrow & I do not understand this one thing.
1. 7^(2x+1)=3^(x+3)
2. 9^(x+2)=2^(5x-4)
3. 3^(4x+3)=8^(-x+2) Please lord help, I have a test tomorrow & I do not understand this one thing.
1. 7^(2x+1)=3^(x+3)
2. 9^(x+2)=2^(5x-4)
3. 3^(4x+3)=8^(-x+2) @Mathematics

Answer 1

You're solving for x :O So yeah. I'll repost this in the morning if nobody knows right now.

Answer 2

take logs of both sides

Answer 3

Hero, my online calculator (not wolfram) shows to use ln? and they got the right answer according to my textbook.

Answer 4

(2x+1)log(7) = (x+3)log(3)

Answer 5

\[\frac{2x+1}{x+3} = \frac{\log(3)}{\log{7}}\]

Answer 6

simplify right side

Answer 7

then continue solving for x

Answer 8

My textbook, shows for its answer: ln(27/7) over ln(49/3), which equals x=.48

Answer 9

You can use ln or logs...doesn't matter

Answer 10

You will get the same answer

Answer 11

But use ln since your book says to use it

Answer 12

The procedure is still the same

Answer 13

I'm still lost. Can you do number two?

Answer 14

When you take logs, whatever is in the exponent comes down from being an exponent and then all you have is just the log of the base of the exponent

Answer 15

I get all that, I just don't get how you actually solved to get x=.48 from that problem.

Answer 16

9^(x+2)=2^(5x-4)

Take logs of both sides:

(x+2)log(9) = (5x-4) log(2)

Divide both sides by (5x-4), then by log(9):

(x+2)/(5x-4) = log(2)/log(9)

Answer 17

I thought you wanted help with the next problem

Answer 18

Okay, I'll finish solving the first problem

Answer 19

I do but i thought you were stil concerntrating on the first. just keep going with #2

Answer 20

First of all, if you're trying to do this without a calculator, not a good idea.

Answer 21

You need a calculator to evaluate log(3) and log(7)

Answer 22

0.56

Answer 23

Yes, now multiply both sides by (x+3) again

Answer 24

2x+1 = .56(x+3)

Answer 25

distribute the .56

Answer 26

.56x+1.68

Answer 27

2x+1 = .56x + 1.6973

Answer 28

And the answer is .48! :D

Answer 29

:D

Answer 30

I thought the answer was supposed to be 48

Answer 31

Oh nevermind, lol

Answer 32

You got it

Answer 33

It wasn't that hard man

Answer 34

Im looking at the 2nd one, and I think i am doing something wrong..

Answer 35

It's the same exact procedure man

Answer 36

(x+2)/(5x-4) = log(2)/log(9)
.31

Answer 37

Also, you can verify your answer by plugging x back in

Answer 38

K so i distribute .31 through 5x-4

Answer 39

and make sure both sides are the same

Answer 40

on the test, plug x back in and verify!

Answer 41

x+2=-1.24+1.55 x

Answer 42

That's the only way to verify that you're right

Answer 43

If you don't do that, you will fail

Answer 44

If you forget to do it, you will fail

Answer 45

x+2=-1.24+1.55 x
x=5.89091

Answer 46

I can promise you that

Answer 47

So make sure to verify your answer tomorrow

Answer 48

I know, thats what I was planning on doing the whole test, just checking constantly.

Answer 49

Good

Answer 50

I just wanted you to confirm that you will do it

Answer 51

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 52

Do not round answers to the end. Never ever round an answer until the end

Answer 53

That's rule #1 of how not to make a mistake on a math test

Answer 54

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 55

Eh, my teacher is lenient and doesn't care as long as you are somewhere in the ballpark.

Answer 56

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 57

Like with a calculator I don't round because I just do 2nd answer, and just input like 50 decimals :P

Answer 58

You're lucky. 99% of most teachers aren't so nice. But still, you want to get as close to the right answer as possible. I wouldn't make it a habit of rounding prematurely man

Answer 59

Don't ever take an online exam where they want the exact answer

Answer 60

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 61

Do you know ANY way of memorzing formulas besides writing them a million times?

Answer 62

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 63

I was thinking of just learning the formulas like before the test, and right when the test starts just write them right on the test..

Answer 64

Yep, you just have to know them man. That's all I can say. Most of it is just algebra anyway

Answer 65

What is the test on?

Answer 66

What chapter or section of math topics does it cover?

Answer 67

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 68

Exponential functions, Logarithmic functions, Properties of Logarithms, Exponential and Logarithmic Equations, and inverses of logarithms/exponential equations

Answer 69

log(a-b) + log(a-b) = ?

Answer 70

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 71

inverse as in y=x+2, then just replacing x for y, y for x, solving for y.
x=y+2, y=x-2, easy.

Answer 72

Well, actually, that's a bad one because the answer to that would just be 2(log(a-b)) which if you further simplify to 2(log(a/b))

Answer 73

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 74

I have no idea what that is :S

Answer 75

you see that they have the same base so you combine them

Answer 76

It's like x + x

Answer 77

= 2x

Answer 78

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 79

oh! I know what that is, i thought you wanted me to name something lmao

Answer 80

except it has an extra step included

Answer 81

Like as if its a property or something, i was like uhhh....

Answer 82

Yeah , but you didn't get it immediately

Answer 83

No, I want you to simplify it

Answer 84

c'mon man, you should know what to do if someone gave you that

Answer 85

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 86

You multiply them btw ;)

Answer 87

You can't put "oh yeah I know what that is" on the test

Answer 88

If they're the same base you can just add and simplify as I showed above

Answer 89

You're forgetting the x + x rule

Answer 90

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 91

ln(x+2)+ln(3x-2)=2ln(2x), you do
ln(x+2)(3x-2)=ln4x^2,
3x^2+4x-4=4x^2
x^2-4x+4=0
quadraticccc

Answer 92

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 93

yeah my teacher sucks she doesnt teach us rules, she just tells us to solve.

Answer 94

ln(3x-2)+ln(3x-2) = ?

Answer 95

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 96

(3x-2)(3x-2)
9x^2-6x-6x+4
9x^2-12x+4

Answer 97

Textbook got 5.65, but they round weird, so 5.89 is close enough :D

Answer 98

or 2ln(3x-2)