Question 1042488
logb(2) = .3562
logb(3) = .5646
logb(5) = .8271


logb(x) = y if and only if b^y = x.


using this formula:


logb(2) = .3562 if and only if b^.3562 = 2
raise each side of the equation to the 1/.3562 power and you get:
(b^(.3562)^(1/.3562) = 2^(1/.3562)
simplify to get b = 7.000274846


do the same with the the other two and you will get b = 6.999...


since b has to the same value in all 3, then my guess is that b = 7.


using that guess, i got the answers indicated when i rounded to 4 decimal places.


for example:


log7(2) = .3562
log7(2) = log(2)/log(7) = .3562
evaluate log(2)/log(7) and you get .356207.....
round it to 4 decimal places and you get .3562.


i was able to get the other answers as well rounded to 4 decimal places when i assumed b = 7.


given that b = 7, the other problems should fall in line.


logb(12) becomes log7(12) which becomes log(12)/log(7) which is equal to 1.276989... which becomes 1.2770 rounded to 4 decimal places.


logb(5b^4) becomes log7(5*7^4) which becomes log7(5*2401) which becomes log7(12005) which becomes log(12005)/log(7) which is equal to 4.8270874...which becomes 4.8271 rounded to 4 decimal places.



logb ^8sqrt(3b) ?????


i'm not exactly sure what to do with this.
did you mean logb(8*sqrt(3b)), or did you mean:
logb^8(sqrt(3b)) ?????


what is the base?
what is the argument of the log?


in logb(x), b is the base, and x is the argument of the log.


if you can't do that, then give it in english, such as log of (sqrt(3b)) to the base of b.


as it stand, i just can't figure it out.