Question

What is the solution to the equation log2 x - log2 4 =5?

Answer 1

u mean log 2x and log 24?

Answer 2

The rules for logarithms is:
n^logn(x) = x

Answer 3

Is the base 2??

Answer 4

\[\log_{2} x = \log_{2} 4 =5\]

Answer 5

* -

Answer 6

rule*
So, when your base is 2 (log2), then 2^log2(x)=x

Answer 7

\[\log _{2} x - \log_{2} 4 = 5\] sorry that is the equation

Answer 8

Okay

Answer 9

See if you can eliminate the logarithms from the equation :)

Answer 10

would it be x - 4 =5?

Answer 11

Not quite, when you use an operation on one side of the equation, you must do it on the other side, otherwise you change the equation.

Answer 12

You are close though :) 2^log2(4)=4 indeed

Answer 13

hm.. what would I do to the other side of the equation??

Answer 14

What did you do to the left side?

Answer 15

I eliminated the log part

Answer 16

How is log2(x) different from x

Answer 17

log2 (x) - log2(4) = 5

log2 (x/4) = 5

2^5 = x/4

Finish her up.

Answer 18

How did 2^5 come out? I'm confused..

Answer 19

log(base) (answer) = (exponent)

2 is the base, 5 is the exponent, x/4 is the answer.

Answer 20

okay

Answer 21

but why would that become 2^5?

Answer 22

where did the log go?

Answer 23

Log is just another way to write out an exponent. So 2^5 is the same thing as log2 (x) = 5.

Answer 24

For the last step he did:
\[2^{log2(\frac{x}{4})}=2^5\]

Answer 25

I see..

Answer 26

Okay, I get it now.. so all I have to do now is to solve for x from 2^5 = x/4 right?

Answer 27

Yep. You got it!

Answer 28

o.o yay thanks!

Answer 29

One more thing-- if there's two logarithms being subtracted do I always just divide them if they have the same base?

Answer 30

Yes. And if they are added with the same base it's multiplication instead.

Answer 31

then if they're multiplied it would be addition? and subtraction if they are divided?

Answer 32

No, I don't remember exactly how it's done off of the top of my head but if the expanded forms are multiplied or divided then you should be able to multuply them together to get your answer.

Let me see if I can remember how it's done.

Answer 33

Okay, thanks :)

Answer 34

I guess I should clarify. If you have something like log(1000/100) then it would be equal to log(1000) - log(100). However, if you have log(1000)/log(100) it is not.

Answer 35

ohh.. i see

Answer 36

That makes a lot sense. Thank you!

Answer 37

Not a problem! =)

I can't remember any shortcut for solving the latter but chances are you won't need a shortcut, just solve each log independently then find the difference of their answers.

Answer 38

Thank you so much :)

Answer 39

\[\boxed{\log_b x+\log_by=\log_bxy}\]\[\boxed{\log_b x-\log_by=\log_b\frac xy}\]

Answer 40

That cleans it up, thank you :)