Question

Consider loga 18 = 2,890 and log 18 = 1,255. So, loga 10 is equal to...?
a) 1,890
b) 2,302
c) 2,032
d) 1

Help pls!

Answer 1

"a" is in the base right?

Answer 2

that's correct

Answer 3

Can we use calculators?

Answer 4

Not sure

Answer 5

Why?

Answer 6

loga 18 = 2,890
log 18 = 1,255
then a^2,890 = 18 and 10^1,255 = 18
so a^2,890 = 10^1,255
what do i do?

Answer 7

loga 10^1,255 = 2,890

Answer 8

what now?

Answer 9

1,255 loga 10 = 2,890

Answer 10

Hey. Sorry i lost my connection.

Answer 11

Np.

Answer 12

SOrry but i dont really get what you did. :(

Answer 13

Well, loga 18 = 2,890 so a^2,890 = 18, right?

Answer 14

Also, if log 18 = 1,255, then 10^1,255 = 18

Answer 15

Why u did a^2 ?

Answer 16

That's log property. logb x = y means b^y = x.

Answer 17

Oho! commas were confusing me!

Answer 18

Well the way i was doing was,
\[\frac{\log18}{\log a} = 2890\]

Answer 19

Mmm I don't get that

Answer 20

let me thinkk.. .q

Answer 21

doint you think it's
log(18) = 1.255 ?
instead of 1,255?

Answer 22

I guess that's right. We use , instead of .

Answer 23

oh man! now i have to do the whole thing again. lol.
i thought that it's thousand..

Answer 24

oh sorry xD I should've known that you guys use .

Answer 25

lol, Yeah. Mostly "." is used.
you should mention it. :)

Answer 26

Yep, I will keep that in mind.

Answer 27

Found it!! !!!!!!!!!!!!!!!!!!! :D
It's B

Answer 28

It's a more mental math question! But it's really really nice one!

Answer 29

please tell me how you got that!!

Answer 30

Can you wait for about 10-15mins?

Answer 31

i will brb.

Answer 32

Sure.

Answer 33

Back! :D

Answer 34

Wb :D

Answer 35

i am doing a mistake, hold on.
i forgot the steps. lol.
but the answer is b

Answer 36

Ok,

Consider loga 18 = 2.890 and log 18 = 1.255. So, loga 10 is equal to...?
a) 1.890
b) 2.302
c) 2.032
d) 1

First of all,

using the log property,
\[\frac{\log18}{ \log a} = 2.890\]

Now they gave you the value for log 18. which is 1.255,
So insert the value in the place of log 18

\[\frac{1.255}{\log a} = 2.890\]This can be written as,
\[\log a = \frac{1.255}{2.890}\]
\[\log a = 0.4343\]
\[\large a = 10^{0.4343}\]
a = 2.718

Answer 37

Now,
\[\log_a 10\]\[\large \log_{2.718} 10\]You will get, 2.302

Answer 38

Phew..

Answer 39

i hope you get it?

Answer 40

mmm whats the first property you used?

Answer 41

Oh I got it

Answer 42

The first property is,
\[\large \log_a b \to \frac{\log b}{\log a}\]

Answer 43

Yep thx I got it

Answer 44

Welcome.

Answer 45

Thank you very much for your help!! You're awesome

Answer 46

Welcome Welcome.
I really liked the format of the question. Loved it infact.

Answer 47

Lol I didn't. :D

Answer 48

Lol.

Answer 49

You used a calc though, didnt you?

Answer 50

YES! How can i do without it?
we have to find the values using logs!

Answer 51

I used it while finding the values of a.

Answer 52

Tell that to the freak that invented this question. I wasn't suppose to use a calc

Answer 53

Haha, then how can we solve \(\Large 10^{0.4343}\) ?

Answer 54

We have to use a calc here. and at one more step. rest all we can do without a calc.

Answer 55

Exactly, haha. Thx

Answer 56

Lol. welcome.

Answer 57

I would never get that alone

Answer 58

:P

Answer 59

I took this question as a challenge! :D

Answer 60

Haha you're awesome indeed!!

Answer 61

Thankyou. ;)

Btw which grade this question is about?

Answer 62

No idea. Probably from 1st year of high school or something

Answer 63

Isn't it your question? o_O
umm, no.. in 1st year of HS algebra is taught?

Answer 64

Yep, I got this question from a list of exercises but it has nothing to do with homework or my school. Mmm... I don't really know, but I remember first learning about logs in 1st year of high school or 1 year earlier.

Answer 65

umm, okay.. nice.