Question

Evaluate each expression. . .

Answer 1

\[\log_{2}(1\32) \]

Answer 2

the answer is -5

Answer 3

\[\log_{2} 2^{-5}=-5\log_{2} 2=-5*1=-5\]

Answer 4

cause 1/32=32^-1=2^-5

Answer 5

okaay, you lost me with the -5 * 1? How did you get that?

Answer 6

\[\log_{a} b ^{c}=c*\log_{a}b \]

Answer 7

the exponent goes in front of the log and multiplies it

Answer 8

I understood that part but how does \[\log_{2}2 \] = 1?

Answer 9

and \[\log_{a}a=1 so \log_{2} 2\]

Answer 10

yea

Answer 11

I stilll don't understand. :( What is \[1solog_{2}2?? \]

Answer 12

\[\log_{a} a=1\]

Answer 13

Oh, always?

Answer 14

yea...\[\log_{58} 58=1\]

Answer 15

and what if it is \[\log_{a}b? \]

Answer 16

then \[\log_{a} b=c\]

Answer 17

so c^a=b

Answer 18

ex: \[\log_{2} 32=5 \]

Answer 19

Because \[2^{5}=32\]

Answer 20

but isn't it c^a=b?
your example looks like a^c=b

Answer 21

sorry it is a^c..sorry..typing mistake :(:(

Answer 22

its okay no worriess:p Okay I get it now, i think. Haha. Thank youu!

Answer 23

I really hope u do :):) and ur welcome :)

Answer 24

I'm sorry to bother you again but I figured you're good with logs:p

Solve each equation:
\[\log_{7}9+\log_{7}-2x=\log_{7}19 \]

The answer is:
\[\left\{ (-19\18) \right\}\]

Answer 25

It's ok i like them :)

Answer 26

haha, i knew it! :p

Answer 27

log_7 of -2x??????

Answer 28

yeep.

Answer 29

okaay. that's weirdd.

Answer 30

w8w8w8w8..let me see again :)

Answer 31

u want to find X right?

Answer 32

there's a rule that says : \[\log_{a} b+\log_{a}c=\log_{a} b*c\]

Answer 33

so \[\log_{7}9+\log_{7} -2x=\log_{7} 19\]

Answer 34

I think? I'm so confused. . .

Answer 35

\[=\log_{7} [9*(-2x)]=\log_{7} 19\]

Answer 36

\[\log_{7}(-18x)=\log_{7} \]

Answer 37

since the bases ar the same we can equal -18x=19 therefore x=-19/18

Answer 38

ohh......

you're amazing you know that?! hahaha

Answer 39

you've saved my retricetwice. Congrats(y)

Answer 40

Hahaha loool :P:P no I'm not...:P

Answer 41

yess you aree. thank you sooo muchh(Y)

Answer 42

Uw :)
(ur not cheating in a test r u?)

Answer 43

No!!! Haha, I have finals-.-

Answer 44

oh...good to hear tht...hmm..let me see if i can give u a link abt log

Answer 45

what if it ends up being \[2x ^{2}-6=44?\]

Answer 46

Thanks!

Answer 47

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

Answer 48

2x^2=44+6
2X^2=50
x^2=50/2
x^2=25
x=+-5

Answer 49

ahh. okaay, correction, 3 timesss(y)

Answer 50

And thanks for the website:p

Answer 51

ur welcome :)
Sometimes it is easier to learn smth from internet than books :P:P

Answer 52

Yeah, that's truee.But what about natural logs?

I have one here that says \[\ln 3+\ln (x-8)=3\]
and i was able to get all the way up to \[\ln 3x-24=3\]

but i dont know what to do from there.

Answer 53

huh?

Answer 54

yea..remember when i told u tht log_a,b^c=c*log_a,b?

Answer 55

yesss.

Answer 56

so 3 is an exponent ...and ln n is=1 so we can say that 3=3*ln n

Answer 57

wait but how did you get 3ln n from 3?

Answer 58

the answer is \[\left\{ (e ^{3}+24)/3 \right\}\]

Answer 59

i explained that above.....
u know that 3=3*1 right...so 1=ln e in this case
we must have log with same base (*e in this case) so we can equal 3x-28

Answer 60

Okay. so ln=e?

Answer 61

hmnmhmhm..can i write it again plsss????????????????
I've done some very stuuuuuuuuupid mistakes

Answer 62

haha, its okay, go ahead. break it down please. I'm kinda stupid on the weekends:p

Answer 63

let me delete all those and I'll explain better

Answer 64

ln(3x-24)=3
ln(3x-24)=3*ln e
ln(3x-24)=lne^3
so base is the same=e and we can equal 3x-24=e^3 we add 24 from both parts
3x=e^3+24 then we divide with 3
x=(e^3+24)/3
the same answer as u have :) got it?
PS: I'm so sorry that i messed u up....i've been studying math all day so..my brain is a bit ''out of order''

Answer 65

Lol, okay I think I get it now, I'm gonna try to do it by myself and see if i get it.

And don't worrry about, I'm out of order too:p

Answer 66

K ^_^ :)
LOL :D

Answer 67

I get it! YAY! :D

Answer 68

Okay, new problem for something completely different or am I boring you and you wanna go sleep?

Answer 69

Happy for you :)(it's 4:13 pm here...no sleep at this time...)
Ur not boring me at all...is just that idk if i'll know how to answer...u ask it anyway

Answer 70

Okay, rofl, its 10 in the morning here, I'm super tired and I have tutoring in an hour-.-

okay, next problem. Solve each equation. Round your answers to the nearest ten-thousandth.
\[3\times19^{1.8x +7}=65\]

Answer 71

10 am and ur tired?????????? oO
is tht x multiplying or as a variable?

Answer 72

yes, 10 am and im exhausted. I normally don't wake up until 12:p
and i really don't know:p

Answer 73

Hahah lool...I wake up at 7am :P
Come on...how u don't know?? Oo

Answer 74

Oh wow. Early riserr.

And I don't know the difference. But if I had to guess I would say variable.

The answer is -3.3086

Answer 75

:P:P:P hmmmmmm...let me work on a paper 1st and see if i can solve it ...

Answer 76

Okaay, you do that and I'll be right back:p

Answer 77

[19^(1.8x+7)]*x=65/3
\[\log_{19} 19^{1.8x+7} * x=\log_{19}65/3 \]

Answer 78

\[(1.8x+7)=\log_{19}65-\log_{19}3-\log_{19}x \]

Answer 79

:(:(:( I'm sorry....Idk how to transform it......:(:(:( I'm really sorry :(:(

Answer 80

It'd b easier if X was ''multiply''

Answer 81

Can u please think if it really is a variable?

Answer 82

its okay dont worry about itt:p

Answer 83

U know...i was thinking u might have gone to bed :P:P
Sorry and thnx :)

Answer 84

Noo, hahaha! But I am going to tutoring now:p Thanks for the helpp! TTYL

Answer 85

Ur welcome... Have a gr8 time,see ya :)