Solve Log Equations with Log Laws: Examples on Logbase 4, 2, and 10

[skg94]

Homework Statement

Solve for x

logbase 4 for question 1.

1. log (x+2) - log (x-4) =1/2

log base 2:

2. log (3x+1) = 2 - log (x-1)

log base 10:

3. log sq root (x^2 -21x) =1

similar just different numbers..

log (x-4) - log (x+2) =4 base 2
log (x-4)=4-log(x+2)
log (x^2-2x)^7=21

Homework Equations

Log laws

The Attempt at a Solution

1. log (x+2)/(x-4) = 1/2 - is that right or is it log (x+2) = 1/2 + log (x-4) then cancel the logs. I don't know. When i tried it both didnt work. Maybe i calculated it wrong if its set up right.
2. (3x+1)(x-1) = 2
3x^2-2x-1=2
3x^2-2x-3 - what do i do from here?

3. If you square both sides, or times the square and x by .5 and equal it to zero, i don't know what to do, same process of solving for the later 3 I am pretty sure I am having difficulty with these.

Any help please

 

[Michael Redei]

1. log (x+2)/(x-4) = 1/2 looks fine. Next step: get rid of the log.

2. (3x+1)(x-1) = 2 -- Here you did just that, i.e. got rid of the log, but only on the left side. You need to fix the right side before you work out (3x+1)(x-1)

3. log( √ something ) = something else ... get rid of the log first:
√ something = 10 ^ (something else) ... square each side:
something = (10 ^ (something else)) ^ 2 = 10 ^ (2 times something else)
This is a quadratic equation which you should be able to solve. (Hint: the number 29 should appear somewhere on the way. If you see that, you're probably getting on okay.)

 

[HallsofIvy]

Are you clear on what a logarithm is? It is the inverse to the exponential function- if y= log_a(x), then x= a^y. So if log₄ A= 1/2, then 1/2= 4^A. What A makes that true?

 

[skiller]

So if log₄ A= 1/2, then 1/2= 4^A. What A makes that true?

Try again.

 

[Michael Redei]

If log₄ A = 1/2, then A = 4^1/2...

 

[HallsofIvy]

Oops!

 

[Mark44]

We all have our days ...

 

[skg94]

i got them all ha it was just simple as getting rid of the log, silly we all do have our days.. thank to all of you though

 

[skiller]

We all have our days ...

Halls seems to have her bad days more often than not!

 

[Mark44]

Halls seems to have her bad days more often than not!

I would disagree on two points:
1. I have rarely seen him make a mistake.
2. Halls is a "he".

 

[skiller]

I would disagree on two points:
1. I have rarely seen him make a mistake.
2. Halls is a "he".

Ok, I would disagree on just the one point. For some reason, I thought HoI was a she.

But I haven't got enough fingers on both hands to count how many errors he's made in the last month or two! (Ok, maybe that's a bit harsh, but for a "PF MENTOR", far more than enough.)