Question

Find x=3³^x 3²^x/3^x=4√3²⁰​

Answer 1

Step-by-step explanation:

please write question on paper

Answer 2

Answer:

If you are talking about real x , you can just write like this:

Since (x+3)3=33

So x+3=3

Therefore x=0

Doing this is totally fine, since cubic root is indeed a bijection from R to R . If you don’t know the word bijection, it just means here that x3−−√3=x for any real number x . Noted that this is not true for square root, (−1)2−−−−−√=1–√=1≠−1 .

But if you are talking about complex number, then you cannot do like this, since you will miss out two complex roots. Instead, it should be:

(x+3)3=33

⇒(x+3)3−33=0

⇒x((x+3)2+3(x+3)+32)=0

⇒x(x2+9x+27)=0

⇒x=0 or x2+9x+27=0

For x2+9x+27=0 , by using the formula x=−b±b2−4ac√2a ,

We get x=−92±33√2i

So all the three roots are 0,−92+33√2i,−92−33√2i .