SOLVING SIMPLE LOG PROMBLEM - al 2 - easy best answer?

Question

Solve 2^(3x - 6) = 8

2^(3*3 - 6) = 8

2^(9-6) = 8

2^(9-6) = 8 is equivalent to 2^(3)



My teacher said i solved this through the process of elimination and asked how to solve if I didn't know x = 3.

What does she mean - please explain .

Answer 1

The left side is a power of 2. So you want to rewrite the right side as a power of 2 also.

We know that:
8 = 2^3

Substitute this on the right side to get:
2^(3x - 6) = 2^3

Now since both sides are raised upon the same base (2), you can just look at the exponents which must be the same:

3x - 6 = 3

Solve this as usual:
3x = 3 + 6
3x = 9
x = 3

Answer 2

Because this is a simple problem, you figured out early on that x =3, so you substituted in 3 for x.

So, if you kept x through the whole problem, you would have to use logs.
2^(3x -6) = 8
now, logs allow you to move the exponent down.
log (3x -6) x 2 = log 8
you see how i took the log of both sides. Now, to get rid of the logs, (if you have a scientific calculator, you use the log button) so...
log (3x -6) x 2 = log 8

log 8 / log 2 = 3
i am dividing the log of 8 by the log of 2 to isolate the variable
so now you have....
3x - 6 = 3
3x = 9
x = 3

hope this helps! :)

Answer 3

You were right to notice that 8=2^3. Since you have a common base and are solving for a variable in the exponent, you could take log base 2 of both sides. log(b^n) =n (that log taken in base b of course). Had you done that, you would have gotten 3x-6=3, then you could just solve for x.

Answer 4

2^(3x -- 6) = 8
=> {2^3}^(x -- 2) = 2^3
=> x -- 2 = 1
=> x = 3

2^(3*3 -- 6) = 2^(9 -- 6) = 2^3 = 8

Answer 5

Get the same base...

8 is 2^3

so you can do the equation

3x-6=3
When you solve this you get x=3..
Im guessing thats what your teacher meant...

Answer 6

well, i guess you know that 2^3 equals eight, so i think your teacher is looking for you to write an equation

3x-6=3

then add six to both sides

3x=9

then divide by three

x = 3

Answer 7

ohhhh this looks really hard