SOLUTION: root of x raised to the power log x equals 100

Algebra.Com
Question 1154501: root of x raised to the power log x equals 100

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

The original equation is

     = 100.


The domain is  { x | x > 0 }.


The equation is equivalent to

     = 100.


Square both sides.   You will get

     = 10000.


Take logarithm base 10 from both sides.  You will get

    log(x) * log(x) = log(10000),   or

    (log(x))^2 = log(10000),  or

    (log(x))^2 = 4.


Take square root from both sides.  You will get

    log(x) = +/- 2.


So we have two solutions

    1)  log(x) = 2,  x =  = 100,   and


    2)  log((x) = -2,  x =  = .


ANSWER.  The original equation has two solutions,  x = 100  and  x = .

Solved.

RELATED QUESTIONS

If x raised to the 27th power equals one million, what is the value of... (answered by reviewermath)
what is seventh root of x raised to the seventh power is x. (answered by Alan3354)
7 raised to the x power parenthesis 7 raised to the 3rd power outside the parenthesis is... (answered by solver91311)
Four raised to the power x plus 6 to the power x equals 9 to the power... (answered by ikleyn)
(1/x)*square root of (1/z (raised to the 5th... (answered by edjones)
solve square root of x raised to the two-thirds power (answered by jsmallt9)
169 raised to the power of 3/2 =13 raised to the power of (x-1) (answered by Alan3354,lwsshak3)
The square root of x raised to the 3rd power divided by the square root of... (answered by jsmallt9)
Determine all the values of x for which: √x^(log10x)=100 (To be read as "the... (answered by Theo)