Question

2^xsquare=4^2x-2

How do I solve this question,please help.

Answer 1

Can you retype the question, i don't get it.

Answer 2

(Use equation editor on the bottom left corner)

Answer 3

\[2^{x2}=4^{2x-2}\]

Answer 4

\[2x~Log~2=(2x-2)~Log~4\]\[2x/(2x-2)=Log~4/Log~2\]

Answer 5

good till now?

Answer 6

Yup,but is it possible to use the indices law to solve this?

Answer 7

Yes yes

Answer 8

\[Log_35=\frac{Log_{10}5}{Log_{10}3}\]see this example?

Answer 9

Yes,I am fairly new to logarithm.Could you help me on that too?

Answer 10

Do you see this example above get it? yes/no

Answer 11

(it a formula/identity)

Answer 12

I don't get it

Answer 13

You are saying that it's = log of number over log of base.

Answer 14

Is this the change of base law?

Answer 15

YES.

Answer 16

Good so far?

Answer 17

yup

Answer 18

look at the left right of you question.\[\frac{Log4}{Log2}\](presumably, when not spesified the base is 10) just like if you see \[\sqrt{?}~~~~~i t's ~~~~~\sqrt[2]{?}\], right?

Answer 19

yes

Answer 20

So it would be the same thing as \[\frac{Log_{10}4}{Log_{10}2}\]

Answer 21

\[\frac{Log_{10}4}{Log_{10}2}=Log_24\]So far so good?

Answer 22

So when you write log it is already known that it's base is 10?

Answer 23

When not indicated otherwise.

Answer 24

Alright

Answer 25

\[Log_24\]good with this one?

Answer 26

\[\frac{Log_{10}4}{Log_{10}2}=Log_24~~~~~~~~~~~~~Good?\]

Answer 27

Yes,but how about this side?\[\frac{ 2x }{\left( 2x-2 \right)}\]

Answer 28

So far we have \[\frac{2x}{2(x-2)}=\log_24\]OK?

Answer 29

Okay,then what's next?

Answer 30

\[Log_bb=1~~~~~~~~~~identity/law\]

Answer 31

\[Log(x \times y)=Log~x + Log~y\]\[Log(4)=Log(2 \times 2)=Log~2 + Log~2\]no matter what the mase is as long as it is the same base.

Answer 32

If I am not mistaken,the above is the product law?

Answer 33

Yes it is, you are correct, so far so good?

Answer 34

Yup

Answer 35

\[With~~base~~2:~~~~~~~~Log_2(4)=Log_2(2 \times 2)=Log_22+Log_22\]\[knowing~~that:~~~~\log_bb=1\]\[Log_22+Log_22=?\]you tell me

Answer 36

Is it 1?

Answer 37

\[Log_bb=1~~~~~~~~~Log_22=1\]\[Log_22+Log_22=1+1=2\]

Answer 38

See?

Answer 39

Do you see how i got \[Log_22+Log_22\]

Answer 40

I get it now,thanks a lot