Question

2log(x-3)+1 = 5

Could you break it down step by step? I'm a bit confused on how to do this algebraically

Answer 1

To solve x?

Answer 2

yes, i presume

Answer 3

Okay, first, subtract both sides by 1, what do you get?

Answer 4

you get 2log(x-3) = 4

Answer 5

Right, now divide both sides by 2, what do you get?

Answer 6

log(x-3) = 2

Answer 7

haha, that's fine :)

Answer 8

Don't mind me. @Callisto seems to be doing a fine job teaching so I'll just observe if you don't mind? I'll only respond if you ask.

Answer 9

Yup! Now, take anti-log for both sides. What do you get?
Note:
anti-log = inverse of log
For example,
logx = 1
=> 10^(logx) = 10^1
=> x = 10^1 = 10

Answer 10

yikes, haha, i'm not for sure. I briefly remember anti-logs but I'm not for sure what do with them

Answer 11

Do you understand that example?

Answer 12

i'm starting to get it. logx = 1. I understand that but not after that

Answer 13

If I may, @Callisto perhaps he'd @Egirl01 would understand if you asked her to change the logarithm form to exponential form. @Egirl01 do you know how to do that.

Answer 14

No, I'm sorry

Answer 15

give me one second

Answer 16

\(\large b^x=y \rightarrow log_by=x \)

Answer 17

log^2 = x-3?

Answer 18

logx = 1 is actually just an example...
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Intuitively, log a number is the value of the power of the base
Let say, I have a number 100, which can be rewritten as 10^2
Now, I take log (base 10) of that number (100), so I'll get 2, since 10 to the power of 2 give me 100.
(Sorry if I make it even worse...)

Answer 19

No, I understand the piece. so if its simply log, then its naturally log10, and the anti-log of log10 is 1/10 right?

Answer 20

anti-log of log 10 is 10.
\[\log^{-1}(log10) = 10\]
anti-log is the inverse of log.

Answer 21

Alright. So then it'd be 10 (x-3) = 2?

Answer 22

No....
How did you get that?

Answer 23

the anti-log of log 10 is 10, so log(x-3) = 2 would turn to 10(x-3) = 2? Obviously that is wrong. I'm a bit lost but you can continue onto the next part of solving the equation. I'll eventually figure what I'm doing wrong

Answer 24

\[log(x-3) = 2\]Take anti-log for both sides:
\[\log^{-1}(log(x-3)) = \log^{-1}(2)\]
Perhaps you can simplify the left first.

Answer 25

I still don't quite follow, but continue on. I'll understand eventually :)

Answer 26

Nope.. It's your turn to work on it... Which part you don't understand ?

Answer 27

how exactly I create the anti-log from log(x-3)

Answer 28

Because you are doing something on both sides... You create anti-log to undo the work of log...

Answer 29

So the anti-log of log10 is 10, right? and the anti-log of 2 is what?

Answer 30

Before answering you question, could you please answer few questions first?

Answer 31

okay

Answer 32

What is log10?

Answer 33

log10 =1

Answer 34

What is log100?

Answer 35

log100 = 2

Answer 36

Can we tell me what number do I have to take log on in order to get 1?

Answer 37

10?

Answer 38

Yes.
So, what number do I have to take log on in order to get 2?

Answer 39

100

Answer 40

Yes! How did you get this answer?

Answer 41

because you inversed it?

Answer 42

Yes!
So, now, can you answer your question? what is \(\log^{-1}2\)?

Answer 43

It is 100

Answer 44

Yes!

Answer 45

So 10(x-3) = 100?

Answer 46

No.
Another set question questions...
What is log10 (again)?

Answer 47

log 10 is 1

Answer 48

You got it right for the right side, it's wrong for the left.

Answer 49

What is \(\log^{-1}log(10)\)?

Answer 50

10

Answer 51

Yes.
What is \(\log^{-1}(log100)\)?

Answer 52

2?

Answer 53

WAIT

Answer 54

100?

Answer 55

Yes!

Answer 56

What is \(\log^{-1} (log1000)\)?

Answer 57

1000

Answer 58

So, we can see that \(\log^{-1}\) of log a number is the number itself, agree?

Answer 59

yes

Answer 60

So, \(\log^{-1} (\log y) = y\), agree?

Answer 61

yes

Answer 62

So, what is \(\log^{-1} (log(x-3))\)?

Answer 63

x-3?

Answer 64

Yes!

Answer 65

Can you simplify the following now?
\[\log^{-1}(log(x-3)) = \log^{-1}(2)\]

Answer 66

x-3 = 100?

Answer 67

Yes! Now can you solve it?

Answer 68

yes

Answer 69

x = 103?

Answer 70

Nice :D and Yes!
Do you understand how to solve this type of question now?

Answer 71

yes! Thank you soooo much for your help! I really appreciate it!

Answer 72

You're welcome :)