Question

Evaluate

Answer 1

\[\log _{2} \frac{ 1 }{ 64 }\]

Answer 2

@amorfide

Answer 3

It's 6 right?

Answer 4

\(\large \bf {
log_{\color{brown}{ a}}{\color{blue}{ b}}=y\iff {\color{brown}{ a}}^y={\color{blue}{ b}}
\\ \quad \\ \quad \\

log_{\color{brown}{ 2}}{\color{blue}{ \frac{1}{64}}}\implies ?
}\)

Answer 5

2=1/64 ?

Answer 6

hmmm 1/64 is less than 1.. .so can't be equals to 2

Answer 7

32?

Answer 8

well.... let us use 64

what would 64 be in a form of say \(\Large 2^\square ?\)

Answer 9

if we change 1/64 to 64
you would be working out
2 to the power of what gives you 64?

since we want 1/64, we know it must be negative power
so we take the negative answer

Answer 10

-6 is the answer?

Answer 11

dunno.. what form did you get anyway?

Answer 12

apply change of base formula \[\huge\rm log_a b = \frac{ \log b }{ \log a }\]
_:D_

Answer 13

true. you could use the change of base as well

Answer 14

Oh so it's -36 for the answer?

Answer 15

did they say without calculator ? nope!
so you can use CALCULTADORA

Answer 16

so ahemmm what do you think is say \(\Large 64=2^{\color{red}{ \square ?}}\)

Answer 17

is it? why not check for yourself if it's or not

Answer 18

6

Answer 19

So is 6 the final answer? That's it?

Answer 20

so it's 6

so \(2^6 = 64\)

that means one sec

Answer 21

\(\large {
log_{\color{brown}{ a}}{\color{blue}{ b}}=y\iff {\color{brown}{ a}}^y={\color{blue}{ b}}
\\ \quad \\ \quad \\

log_{\color{brown}{ 2}}{\color{blue}{ \frac{1}{64}}}=\square \implies {\color{brown}{ 2}}^\square =\cfrac{1}{64}\implies 2^\square =\cfrac{1}{2^6}
\\ \quad \\
recall\implies \cfrac{1}{a^{\color{red} n}}\implies a^{-{\color{red} n}}\qquad thus
\\ \quad \\
2^\square =\cfrac{1}{2^{\color{red}{ 6 }}}\implies 2^\square =2^{\color{red}{ -6}}
}\)

so.. what do you think it's is then?

Answer 22

Is it going to be positive or negative?

Answer 23

heheh... is right there... is going to bite on the nose

keep in mind that, the choices are there as guides only
they must match your answer, not the other way around

Answer 24

So the answer is -6

Answer 25

\(\bf 2^\square =\cfrac{1}{2^{\color{red}{ 6 }}}\implies 2^\square =2^{\color{red}{ -6}}\impliedby \textit{notice the EQUAtion, meaning}
\\ \quad \\
\square ={\color{red}{ -6}}\)

the bases are the same
is and equation
that means both sides are equal

so, the exponents must also be equal

Answer 26

Ok thanks. :)

Answer 27

yw

Answer 28

\(\color{blue}{\text{Originally Posted by}}\) @jdoe0001
is it? why not check for yourself if it's or not
\(\color{blue}{\text{End of Quote}}\)
sure