Question

1) log x^2 with base 6 = 4 help me please
2) log x^1/2 with base 2 = 1/2
3) 8^(x^2-x) = 32 ^(1-x)

Answer 1

so you know
\(\Large \log_ab=c \implies b=a^c \)
?

Answer 2

Hey, you again :)

Answer 3

hi, yes :)

Answer 4

yes. you're amazing the way you teach, youll let the viewer understand

Answer 5

thank you for the compliment!
i feel happy when i make someone understand something :)

Answer 6

so ,what about log x^2 with base 6 = 4
?

Answer 7

6^4 = x^2?

Answer 8

and you were typing something ? feel free to interact :)

Answer 9

absolutely correct!
just take square root on both sides to get 'x'

Answer 10

so which 2 values of x did u get ?

Answer 11

soo its 36! ^_^

Answer 12

am i right?

Answer 13

yes! and other value ?

Answer 14

oh, wait!

Answer 15

is there any other value?

Answer 16

yes,
x^2 = 36^2
----> x^2-36^2 = 0
(x+36)(x-36) =0
x = -36, x=36
got this ?

Answer 17

while taking square root we consider both \(\pm\) values

Answer 18

make sense ?

Answer 19

anyway why is it that 36 was raised by 2?

Answer 20

6^4 = (6^2)^2 = (36)^2

Answer 21

number 2 pleasee

Answer 22

\[\log_2(x^2)=\frac{1}{2}\]
Try write in exponential form.
\[\log_a(y)=x \text{ equivalent to } a^x=y \]

Answer 23

2^1/2 = x ^ 1/2

Answer 24

2^1/2 = x ^ 1/2

Answer 25

the inside of the log is x^2, correct?

Answer 26

well for my problem it is

Answer 27

for your problem above inside is x^1/2

Answer 28

Ok what does that imply x is?

Answer 29

\[x^\frac{1}{2}=2^\frac{1}{2} \]
just look by inspect...
what would x have to be in order for both sides to be the same.

Answer 30

so x would be 2/? thanlks

Answer 31

yes x would be 2 since 2^1/2=2^1/2

Answer 32

how about my problem number 3

Answer 33

Write 8 as 2^something
Write 32 as 2^something

Answer 34

Goal get the same base on both sides.

Answer 35

2^1=2
2^2=2*2=4
2^3=2*2*2=4(2)=8
2^4=2*2*2*2=8(2)=16
....
What is 2^5?

Answer 36

8 as 2^3 and 32 = 2 ^ 5

Answer 37

yes

Answer 38

\[2^{3(x^2-x)}=2^{5(1-x)}\]

Answer 39

if a^x=a^y then a=y.

Answer 40

So set your exponents equal and solve for x.

Answer 41

so 3 (x^2 - 3x) = 5(1-x) shall i distribute it?

Answer 42

yes

Answer 43

3x^2 - 3x = 5 = 5x what would be next?

Answer 44

3(x^2-x)=5(1-x)
3x^2-3x=5-5x
Put everything on one side.

Answer 45

3x^2 + 2x = 5?

Answer 46

Ok then subtract 5 on both sides.
You can then use the quadratic formula.

Answer 47

you mean 3x^2 + 2x - 5 = 0 than factor it out?

Answer 48

You can use quadratic formula or factoring.

Answer 49

how is it done please

Answer 50

i find it hard on factoring

Answer 51

What two factors of a*c have product ac and sum b?
What two factors of -15 have product -15 and sum 2?

Answer 52

gonna finish it tomorrow, i'll study this buy tomorrow for it's time for me to sleep. it\s already 1 am here. how about there?

Answer 53

thankyou so much for helping me. see ya

Answer 54

noon time

Answer 55

aw, yeah, so goodbye for bow. I'll be right back. thankyou so much! its time for me to sleep

Answer 56

*now

Answer 57

have sweet dreams! :)