HELP PLZZZ!!
log(4x+10)=3

Question

HELP PLZZZ!!
log(4x+10)=3

anonymous · Answer

@phi

kamille · Answer

i think you made  a mistake writing the problem. can you rewrite it?

anonymous · Answer

its correct

kamille · Answer

it cant be just "log" without a base

anonymous · Answer

its always 10

phi · Answer

I would assume log means log base 10

anonymous · Answer

yes it does

kamille · Answer

there must be a small number like:

$$\log _{1}23$$

kamille · Answer

lg is log_10(10)

anonymous · Answer

what phi said its log base 10

phi · Answer

you can "undo" the log
log(4x+10)=3
can be written as
4x + 10 = 10^3   

10^3 is 1000
so the problem is 
4x + 10= 1000
can you finish ?

kamille · Answer

@Phi don't you use "lg" instead of log_10(10)?

anonymous · Answer

247.5?

phi · Answer

lg seems to be a newer "standard" way of writing log base 10.  But log (without a base) most often means log base 10.   To add to the confusion,  sometimes you see lg referring to log base 2.

kamille · Answer

oh, it is so different all over the world. Do you know what is ln?

phi · Answer

to solve
4x + 10= 1000
add -10 to both sides

4x + 10 -10 = 1000 -10
simplify:  on the left 10-10 is 0,  and on the right 1000-10 is 990.  you get

4x = 990
divide both sides by 4
x = 990/4 = 247.5

you can check this number in the original equation
log(4*247.5+10)=3
and see if you really do get 3

phi · Answer

@Kamille See http://en.wikipedia.org/wiki/Logarithm#Particular_bases in particular, the column labeled "other notations" for common variations on how to abbreviate log to some base.