log (x^2)+log (x^4) / log(100x) = 2

Question

Just need to what x is equal to and how

Answer 1

Hi Steph,

 

x = 10.  Here is how:

 

log (x²) + log (x⁴)   =   2

      log 100x

 

power comes out to front:

 

2 log x + 4 log x   =   2

      log 100x

 

 6 log x    =    2

log 100x

 

  6 log x   =   2

log 10² x

 

power comes out to the front again

 

6 log x    =   2

2 log x

 

why only log? because log without any base is same as log base 10

 

3 log x   =   2

1 log x

 

3 log x - log x = 2

 

2 log x = 2

 

log x = 1

 

because log without any base is same as log base 10, 10¹ = x,

Which means x = 10.

 

Let's check it:

 

log 10² + log 10⁴   =   2

    log 100 * 10

 

100 * 10 = 1000 = 10³

 

log 10² + log 10⁴   =   2

       log 10³

 

Since all logs share same base (10), they will get canceled:

 

2 + 4   =   6   = 2

   3           3

 

It work out.  Good luck to you.