Question

How do I convert y=100*2^x into Log form?

Answer 1

More importantly, where does the 100 go?

Answer 2

Sorry, 100*(2^x)

Answer 3

\[100 \times 2 ^{x}\]
=\[\ln \frac{ y }{ 100 } = x \ln 2 . \]
\[x = \ln \frac{ y }{ 100 } \div \ln 2 .\]

Answer 4

divide y by 100

Answer 5

The end is in log form?

Answer 6

change the symbol ln to log it won't matter the the base differs from e to 10

Answer 7

\[\ln = \log_{e} \]

Answer 8

i took log to both sides or ln

Answer 9

gotcha, so what was the end in Log, but more importantly, how did you get that?

Answer 10

So would it be x=Log(2)Y/100?

Answer 11

\[2^{x}= \frac{ y }{ 100 }\]
take the log for both sides
\[\log 2 ^{x} = \log \frac{ y }{ 100 }\]
and use property that
\[\log 2 ^{x} = x \log 2.\]
and divide by log2

Answer 12

man when we write log we mean it is for the base 10

Answer 13

so the base is constant for all = 10

Answer 14

you can solve it in another way like \[2^{x} = \frac{ y }{ 100 }\]
by definition \[\log_{2} \frac{ y }{ 100} =x \]

Answer 15

you are right

Answer 16

I understand what I did up until the y/100, can you explain that at all?

Answer 17

OK let's explain the second method first
for the definition of the log
\[a ^{b} = c\]
thus
\[\log_{a}c = b\]
and change this symbols into yours.

Answer 18

where will the 100 go?

Answer 19

It will stay as it was. why do you want to change it??

Answer 20

No, I just dont know where it would go because it doesnt look like it fits anywhere? is it part of a? I am confused

Answer 21

\[a ^{b} = 2^{x} =c = \frac{ y}{ 100 }\]
as 100 doesn't have the power x

Answer 22

So it y just gets divided by it?

Answer 23

Lets forget about that one. What happens in your original answer after we log both sides?

Answer 24

i use the property of \[\log a ^{b}= b \log a \]

Answer 25

So we have log(2)x=xLog(2)

Answer 26

But is that with a base of 10?

Answer 27

yea when say just log without bases we mean that the base is 10.My textbook does that always and i have never seen \[\log_{10} \] anyway it won't matter(if you wrote it or not

Answer 28

So the end is..? I think im getting it

Answer 29

you can take log with any base put for 10 or e are so common and easier to deal with.You will see ln for both sides in physics a lot as its graph is well-known.
write the problem for the start and try to apply what you understand and give full steps.

Answer 30

So we started with 100*2^x=y
and now we have xLog(2)=y/100?

Answer 31

you took log for both sides not only one ,so log (y/100)

Answer 32

And that is the final answer with a base of 10?

Answer 33

@Catch.me

Answer 34

yea (you can make it any base by constant in both sides)

Answer 35

Thank you so much!

Answer 36

you are welcome :D

Answer 37

x log 2 = Log (y/100) Final answer right? @Catch.me

Answer 38

right and it would be better if you make x in an isolated term to make it at the final = the answer which is gotten from the definition.
\[x= \log_{2} \frac{ y }{ 100 }\]
by using the property
\[\log_{a} b = \frac{ \log_{c} b }{ \log_{c}a }.\]

Answer 39

But the base is no longer 10 is it?

Answer 40

for which equation (write your thinking)
c be what ever it is just it has to be constant for both.
in your method by taking log for both sides c = 10.

Answer 41

I just need it to be a base of ten, so im guessing it is all good, thanks for walking me though it!

Answer 42

so you understood it.
so check the properties of the logs there
http://tutorial.math.lamar.edu/Extras/AlgebraTrigReview/LogProperties.aspx
try yourself first then check it :D