Question

log base 2 fifth root of 32 ?!?!?!?!?!??!?!?!?!!?!??! PLEASE HELP

Answer 1

\[\log_{2} \sqrt[5]{32}=\log_{2}2=1\]

Answer 2

what?

Answer 3

how did you get log base 2 then 2?

Answer 4

the fifth root of 32 is 2, because
\[2^5=32\]

Answer 5

then shouldn't the answer be five ?

Answer 6

so your job is to find
\[\log_2(2)\] which asks the question, "what power do you raise the number "2" to to get an answer of 2?"
and the answer is clearly 1

Answer 7

\[\log_2(2^5)=5\] yes

Answer 8

but you have
\[\log_2(2)\]

Answer 9

wait..what?!

Answer 10

\[2^{y} = 2^{5} \]

Answer 11

ok lets go slow

Answer 12

if your question was
\[\log_2(2^5)\] the answer would certainly be 5 correct?

Answer 13

i.e.
\[\log_2(32)=5\]

Answer 14

wait one sec let me soak this in

Answer 15

ok

Answer 16

so you're telling me that 2^5 does not equal fifth root of 32?

Answer 17

yes i am. 2^5 = 32 not the fifth root of 32

Answer 18

so what is it? and how would u find what it is ?

Answer 19

i want to know the fifth rote of 32

Answer 20

but since 2^5 = 32 then we know that
\[\sqrt[5]{32}=2\]

Answer 21

it is 32^ 1/5

Answer 22

you can think of it that way, yes

Answer 23

im not understanding what you're telling me

Answer 24

which means
\[(32)^{\frac{1}{5}}=(2^5)^{\frac{1}{5}}=2^1=2\]

Answer 25

in english:
two the the fifth power is 32, therefore the fifth root of 32 is 2

Answer 26

i think i understand that. thank you very much. can you help me with a few more?

Answer 27

post i will reply

Answer 28

\[3 \log _{7} \sqrt[6]{49}\]

Answer 29

ok lets do this the easy way.
first of all
\[\log(x^n)=n\log(x)\]

Answer 30

yep. i understand tha : - )

Answer 31

and we can rewrite
\[\sqrt[6]{49}\] as
\[49^{\frac{1}{6}}\] yes?

Answer 32

ummm im kind of confused on those

Answer 33

is that just a general rule ?

Answer 34

you need to understand exponential notation for logs, because logs are exponents.

Answer 35

yes for example
\[\sqrt{x}=x^{\frac{1}{2}}\]
\[\sqrt[3]{x}=x^{\frac{1}{3}}\] etc

Answer 36

and in general
\[\sqrt[n]{x}=x^{\frac{1}{n}}\]

Answer 37

okay awesome. just wrote that on my rules sheet XD

Answer 38

so we start with
\[3\log_7(49^{\frac{1}{6}})\] and then bring the 1/6 right out front as a multiplier (coefficient)

Answer 39

\[\frac{1}{6}\times 3\log_7(49)\]
\[\frac{1}{2}\log_7(49)\] and idea what to do next?

Answer 40

i really have no idea :(

Answer 41

how can you write 49 with an exponent?

Answer 42

what would u do if you have a number in front of the log? like the 1/2

Answer 43

hold on, lets just take care of the 49 first. we can do this problem a different way second

Answer 44

we would write
\[49=7^2\]

Answer 45

and then you have
\[\frac{1}{2}\log_77^2)\] which should be easy now

Answer 46

how would we incorporate the 1/2?

Answer 47

since
\[\log_b(b^n)=n\]

Answer 48

but its 1/2 log

Answer 49

we leave it for a moment. the one half out front is just a number, let it sit there

Answer 50

so the answer is 2

Answer 51

we get
\[\frac{1}{2}\log_7(7^2)=\frac{1}{2}\times 2\]

Answer 52

the answer to
\[\log_7(7^2)=2\] and then
\[\frac{1}{2}\times 2=1\]

Answer 53

oh okay!!!!! wow i get that!

Answer 54

if you like we can do this problem a different way, but maybe one way is enough, you tell me

Answer 55

answer is 1

Answer 56

yes it is 1

Answer 57

i like this way. do u mind helping me with more?

Answer 58

go ahead

Answer 59

\[50 \log 5 \sqrt{125} \]

Answer 60

so we would have

Answer 61

5 ^ x = square route 125 ^ 50?

Answer 62

oh yikes leave the 50 out front!

Answer 63

i mean you are right, but leave it there to make your life easier. think of how to write 125 as a number raised to a power

Answer 64

okay. lol so i have 50 log base 5^x = 5^ 3

Answer 65

i believe that is wrong

Answer 66

close, you just forget the square root

Answer 67

but i don't have the square route anymore i got it al out of the square rote

Answer 68

\[125=5^3\] and so
\[\sqrt{125}=5^{\frac{3}{2}}\]

Answer 69

i dont understand that

Answer 70

just a moment ago we found out that
\[\sqrt{x}=x^{\frac{1}{2}}\] right?

Answer 71

\[\sqrt{125}=125^{\frac{1}{2}}=(5^3)^{\frac{1}{2}}=5^{\frac{3}{2}}\]

Answer 72

yes. oh okay i understand

Answer 73

so then what would we have

Answer 74

so now we have
\[50\log_5(5^{\frac{3}{2}})\]
\[50\times \frac{3}{2}\] etc

Answer 75

as soon as you say
\[\log_b(\text{whatever})\] you should think of ways to write "whatever" as a power of b

Answer 76

*see

Answer 77

oh okay!!! wow!

Answer 78

can u give me an example to try?

Answer 79

\[\log_3(\sqrt[5]{27})\]

Answer 80

can u do one with a number in front of the log

Answer 81

the number out front does not really make any difference, but if you like i can write
\[10\log_3(\sqrt[5]{27})\]

Answer 82

okay let me get my paper lol

Answer 83

6?

Answer 84

yup!

Answer 85

OMG

Answer 86

really? i got it right?

Answer 87

don't be so shocked, you will get the hang of it

Answer 88

can u help me with more? lol

Answer 89

after a couple practice problems you will think "not much to this"

Answer 90

ok we can do another before i go

Answer 91

\[\log _{3} 4 - 1/2 \log _{3} (6x-5)\]

Answer 92

holy moly what are the instruction, write as a single log?

Answer 93

lol i have no idea what to do at all

Answer 94

first you need to make sure what the instructions are. what does it say before the problem?

Answer 95

all it says is : solve

Answer 96

maybe u an help me with a different one instead?

Answer 97

you cannot "solve' because there is not an equation here. maybe it says "write as one log"

Answer 98

which we can do if you like