# Log questions

Tags:
1. Oct 11, 2014

### Alykayy

1. The problem statement, all variables and given/known data
Solve for X

logx-log(x+11) = -1

and

log4x-log4(x+15) = -1

2. Relevant equations

3. 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: Oct 11, 2014
2. Oct 11, 2014

### Staff: Mentor

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. Oct 11, 2014

### Ray Vickson

What "base" of logs is used in the first question?

Anyway, you certainly cannot have what you wrote, which was
$$\log \left( \frac{x}{x} + 11 \right) = -1$$
which gives $\log(12) = -1$. Did you mean
$$\log\left( \frac{x}{x+11} \right) = -1?$$
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. Oct 11, 2014

### Alykayy

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