problem with log2√2=16√2

[sick dew]

i dont know what should i power to 2√2 to get 16√2

[tiny compass]

$$A={x∈R: |x-3| < 6}, B=A={x∈R: x > log2√2=16√2}. Write A′∩B$$

[finite basin]

lebedevhh

[sick dew]

i ended at this point and i don't know what should i do next

[tiny compass]

what is the meaning of the following statement : $$A′∩B$$

[finite basin]

lebedevhh

[tiny compass]

especially the $$A`$$ the prime thing

[finite basin]

lebedevhh

[sick dew]

complement of a set

[tiny compass]

meaning all the elements out of A ?

[sick dew]

i actually dont know

it mean "prime"

[tiny compass]

What is the Complement of a Set? The complement of set A is defined as a set that contains the elements present in the universal set but not in set A

[sick dew]

yes, thats it

[tiny compass]

so you need to find the set representing the A. In other words, you need to solve this equation : $$|x-3| < 6$$

[finite basin]

lebedevhh

[tiny compass]

then take the complement of it

meaning the equation : $$|x-3|>6$$

[finite basin]

lebedevhh

[sick dew]

i actually did it but i dont know how to solve $\log_{2\sqrt2}(16\sqrt2)$?

[finite basin]

Heisenburger

[tiny compass]

$$x > log_{2}√2=16√2$$

[finite basin]

lebedevhh

[tiny compass]

this ?

I think u miswrote it

[sick dew]

that it looks in book

[tiny compass]

ha kk

[sick dew]

this photo was taken by my friend but i don't know where these 3 came from

[tiny compass]

this proprerty of logarithm is vry intersting : $$\log_{b^n}a^m = \frac{m}{n} \log_b a$$

[finite basin]

lebedevhh

[tiny compass]

Perhaps u can use this property to solve the problem

I got it from this website : https://www.cuemath.com/algebra/properties-of-logarithms/

[sick dew]

okay, give me a second

😭

i still cant solve this

[tiny compass]

ok lemme try give me a minute

solved it : x > 3

$$x > 3 $$

[finite basin]

lebedevhh

[sick dew]

ya but how 😞

[tiny compass]

ok bear with me a sec

do u know the exponent rules ?

[sick dew]

let's say that yes

[tiny compass]

the ones u need to solve this problem is : $$x^{a+m}=x^a * x^m$$

[finite basin]

lebedevhh

[tiny compass]

also I recall the log rules that I showed earlier

first of all : $$ 2 * \sqrt{2} = 2^{\frac{3}{2}}$$

[finite basin]

lebedevhh

[tiny compass]

do you understand that ? @sick dew

[sick dew]

yes

[tiny compass]

also $$16 = 2^4 \iff 2^4\cdot \sqrt{2} = 2^{9/2}$$

[finite basin]

lebedevhh

[tiny compass]

do you understand that ?

@sick dew

[sick dew]

yes

[tiny compass]

so we got $$(log_{2^{\frac{3}{2}}} {2^{\frac{3}{2}}) * 3$$

[finite basin]

lebedevhh
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[sick dew]

it scares me

but continue

[tiny compass]

$$(log_{2^{\frac{3}{2}}} {2^{\frac{3}{2}} = 1$$

[finite basin]

lebedevhh
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tiny compass]

using this property

you can tell to ur friend that he was right

[sick dew]

I think that he's a robot or sth 💀

thank you so much

[edgy swallow]

,,\log_{2\sqrt2}16\sqrt2=\frac{\log_{\sqrt2}16\sqrt2}{\log_{\sqrt2}2\sqrt2}=\frac{\log_{\sqrt2}\sqrt2^9}{\log_{\sqrt2}\sqrt2^3}=\frac93=3

[finite basin]

mtt07734

[edgy swallow]

.solved deleted user