2log(base8)4-(1/3)log(base8)8=x

- smurfy14

2log(base8)4-(1/3)log(base8)8=x

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- anonymous

What number are both 8 and 4 a power of?

- myininaya

log(base8)4^2-log(base8)8^(1/3)=log(base8)[4^2/8^(1/3)]

- anonymous

Are you good now smurfy?

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## More answers

- smurfy14

sorry for late response i didnt see my new notifications! um i get what myininaya did but what would you do after that?

- myininaya

simplify!

- myininaya

=log(base8)[16/2] i will let you do the last step

- myininaya

or last two steps

- smurfy14

so x=1 correct?

- myininaya

:) YES!

- smurfy14

whoo thanks so much!

- smurfy14

think you could help me with one more?

- myininaya

ok

- smurfy14

2. Jamal has a game with 2 groups of tiles. The first group of 26 tiles is labeled with all the letter of the alphabet, The second group of 10 tiles is #0-9. If Jamal draws one letter tile and one # tile at the random, what is the probability that he will draw a letter in his name and an odd number?
A. (1/13) B. (5/52) C. (1/4) D. (7/26)

- myininaya

i got 17/26 :(

- myininaya

let me think about it

- smurfy14

ok and ya all the answers tht i was getting werent on there either :P

- myininaya

i suck at probability, but give me a few and I will think

- anonymous

I get A

- smurfy14

could u plz explain it to me?

- myininaya

did you P(AUB)=P(A)+P(B)-P(A and B)

- anonymous

No, I used the probability of two independent events is their product.

- anonymous

So how many ways can Jamal draw a letter that is in his name?

- smurfy14

jaml

- myininaya

its independent events because A has nothing to do with B good thinking bond

- anonymous

right, so 4/26

- smurfy14

someone explain how rhey got A!

- myininaya

dont worry about A

- anonymous

Now, how about the probability of pulling an odd tile?

- smurfy14

1/10

- myininaya

how many odd numbers are between 0 and 9?

- smurfy14

ohhhh ODD 5/10!

- myininaya

ok so since they are independent events you multiply the (5/10)(4/26)

- smurfy14

ok see ididnt get it bc ithought it said 1/10 not 5/10 imissedthe odd part lol thanks!!

- myininaya

lol

- smurfy14

one more q! 3^2x=7^(x-1)

- anonymous

Eeek, that doesn't look good...

- smurfy14

hahaha

- myininaya

q! is read as q factorial?

- myininaya

jk lol i know you mean another question!

- myininaya

take the natural log of both sides

- smurfy14

you mean get the decimal form of both? if so thats what i did but for some reason i came out with a negative # :(

- myininaya

ln3^(2x)=ln7^(x-1)

- myininaya

2xln3=(x-1)ln7

- myininaya

2xln3=xln7-ln7

- myininaya

2xln3-xln7=-ln7

- myininaya

x(2ln3-ln7)=-ln7

- myininaya

x=-ln7/(2ln3-ln7)

- myininaya

x=-ln7/(ln8-ln7)

- myininaya

x=-ln7/(ln(8/7))

- smurfy14

ok i see so b4 i write the work does the answer comeout positive?

- myininaya

you have a negative in front of it so its negative

- smurfy14

ok so were allowed to have a negative as the answer?

- myininaya

ln(negative)=does not exist ln(0) does not exist -lna exist if a>0

- smurfy14

so the answer is?

- myininaya

the answer to?

- myininaya

are we still talking about the previous solution?

- smurfy14

ya the one with the negative

- myininaya

so you are saying its not a solution? why do you say that?

- smurfy14

what? i just want to know what you got for the answer lol

- myininaya

we can check it to see

- smurfy14

youre confusing me

- myininaya

you want to know if it is a solution. if you ever have doubt about something, check it

- smurfy14

no i dont want to know if it is a solution i just want to know the answer lol so would the answer be "no solution"?

- myininaya

give me just sec and i will check k??

- myininaya

it is a solution if i did each step correctly

- smurfy14

so the final answer is....?

- smurfy14

you know like x=?

- myininaya

i can scroll back up and look just sec

- myininaya

it says x=-ln(7)/(ln(8/7))

- smurfy14

so if you put that in your calc what is the number? (sorry i dont have a good calc with me)

- myininaya

> evalf(solve(3^(2*x) = 7^(x-1)));
-7.742930467
>

- smurfy14

ok thanks!

- myininaya

smurfy it is not easy to check the solution, but it is the solution because exponential functions are continuous everywhere

- myininaya

but logarithmic functions are not continuous everywhere log(baseb)x=lnx/lnb so whenever the base is 1 or negative or 0 and whenever x is negative or 0, the the function is undefined

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