Log questions

  • Thread starter Alykayy
  • Start date
  • Tags
    log
  • #1
2
0

Homework Statement


Solve for X

logx-log(x+11) = -1

and

log4x-log4(x+15) = -1

Homework Equations




The Attempt at a Solution


log x - log (x+11) = -1
log (x/x+11) = -1

I don't know how to solve for X after this point

log4x-log4(x+15) = -1
log4 x/(x+15) = -1


I don't know how to get the X out of the log to solve for X
 
Last edited:

Answers and Replies

  • #2
33,712
5,411

Homework Statement


Solve for X

logx-log(x+11) = -1

and

log4x-log4(x+15) = -1

Homework Equations




The Attempt at a Solution


log x - log (x+11) = -1
log (x/x+11) = -1

I don't know how to solve for X after this point

log4x-log4(x+15) = -1
log4 x/(x+15) = -1


I don't know how to get the X out of the log to solve for X
The relationship you need for both problems is this one:
loga(x) = y is equivalent to x = ay.

For your first problem, log means log10 (lob base 10).
 
  • #3
Ray Vickson
Science Advisor
Homework Helper
Dearly Missed
10,706
1,728

Homework Statement


Solve for X

logx-log(x+11) = -1

and

log4x-log4(x+15) = -1

Homework Equations




The Attempt at a Solution


log x - log (x+11) = -1
log (x/x+11) = -1

I don't know how to solve for X after this point

log4x-log4(x+15) = -1
log4 x/(x+15) = -1


I don't know how to get the X out of the log to solve for X
What "base" of logs is used in the first question?

Anyway, you certainly cannot have what you wrote, which was
[tex] \log \left( \frac{x}{x} + 11 \right) = -1[/tex]
which gives ##\log(12) = -1##. Did you mean
[tex] \log\left( \frac{x}{x+11} \right) = -1?[/tex]
If so, use parentheses, like this: log(x/(x+11)) = -1. At his point it matters what base you are using for log.

For a given base ##b##, what number, ##y##, has ##\log_b(y) = -1##? Think about what that actually means.

BTW: either use X or x, but not both in the same problem.
 
  • #4
2
0
I figured them out, thank you.

log x - log (x+11) = -1
log (x / (x+11)) = -1
x/(x+11) = 10-1
x/(x+11) = 0.1
x=0.1(x+11)
x=0.1x+1.1
x-0.1x=1.1
0.9x=1.1
x=1.222...

log4x-log4(x+15) =-1
log4(x/(x+15) = -1
x/(x+15)= 4-1
x/(x+15) = 0.25
x=0.25(x+15)
x=0.25x+3.75
x-0.25x=3.75
0.75x=3.75
x=5
 

Related Threads on Log questions

  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
11
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
6
Views
943
  • Last Post
Replies
4
Views
2K
Top