Question

Can anyone help me with this problem and explain how to do it?
Solve for x.
log(50x+300)=7

Answer 1

- so if i remember correct log(50x+300) so here logarithm is with base 2
- so than we need writing 7 in the form of logarithm with base 2 and this will be log(2) on exponent 7

Answer 2

- in this case

log(50x+300)=log(2)7 where 7 is the exponent and than will be
(50x+300)=128 where 128 is 2 on exponent7
50x+300=128 so now subtract from both sides 300
50x+300-300 = 128-300
50x= - 172 divide both sides by 50
x= - 172/50 simplify by 2
x= - 86/25

Answer 3

ok ?

Answer 4

where did you get the two from?

Answer 5

check it in your math booke when you write log(x) this signe logarithm in the base 2 and
log(2)=1 so hence 7=log(2) on exponent7

Answer 6

I thought if it didn't specify a base, it was 10?

Answer 7

logarith in base 10 have wrote lg

Answer 8

logarithm sorry

Answer 9

so i have checked it on wikipedia now and there is wrote that lg is logarithm the base 10 and log without base notification signe logarithm on the base 2

Answer 10

and hence we can writeing 7=log(2)7 what is logarithm from 2 on the power 7

Answer 11

I'm sorry but if you do it your way jhonyy9, and plug the answer back into the equation, it doesn't come out right.

Answer 12

@Alfie, do you have any idea how to solve this problem?

Answer 13

alfie please check it on wikipedia how is correct this notification of logarithm

Answer 14

log(50x+300) = 7
50x+300 = 10^7

Divide by 50 each member, getting:

x+6 = 200000
x = 199 994

This is the answer with base 10.

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Nevertheless, you can think about it to be with base "e"
Which brings you to:

50x+300 = e^7
x = 1/50 (e^7 - 300)

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I've checked on wikipedia, but there is also the "Other notations" which says logx can be used also as base10 or basee.
For example my calculus teacher uses "logx" just and only for natural base logs.

Answer 15

Anyhow, on your textbook should be specified how the book uses "logx" with no base written. Check it out so that you can understand why your solutions do not match, even though you did the math right!

Answer 16

so and than ln what sign for you ?

Answer 17

ln is base "e" . And untill high school I've been using logx as base 10. My calculus teacher uses logx as natural log and plugs in the base in any other stuff.

While I never used the notation "lgx".

I just wrote "logx" in wolfram alpha, it lets you pick between base 10 and base e. So it's kind of a mess. As I said I think he should compare the solutions with his textbook, where of course a specific notation will be chosen.

Answer 18

ok but wikipedia specify that lg is the base 10

Answer 19

and ln is the base e

Answer 20

log(50x+300)=7

10^log(50x+300)=10^7
50x+300=10^7
50x=10^7-300
x=(10^7-300)/50=199,994

Answer 21

Agreed. As a matter of fact ln is in base "e" of course, same stuff with lg is base 10.
Problem pops up with "logx"

http://en.wikipedia.org/wiki/Logarithm#Particular_bases

Check the "other notations", logx can be used in every situation and it kinda gets a different base.

Answer 22

so from this resulted that i have learned exactly how the wikipedia specify but this all are differents how you have learned in your schooles ,... right ???

Answer 23

Looks like so. I guess the best thing to do in order to get the result right, is to check which base your textbook uses. My calculus textbook (and my calculus teacher) uses logx for natural log.
Now, he should check which notation his textbook uses and do the exercise accordingly :)

Answer 24

ok thank you for your all comments

good luck

bye

Answer 25

Thank you too :)
See you around openstudy :D