Question

X^2logx = 10x^2 solve

Answer 1

Given: x^(2 logx) = 10x²

To find: Solve the above expression.

Solution:

• Now as we have given that x^(2 logx) = 10x², so now we need take log  on both sides.

• So taking log  on both sides, we get:

             log { x^(2 logx) } = log { 10x² }

• Now using the property log ab = log a + log b

             2 log x × log x = log 10 + log (x²)

• Now using the property log a^b = b log a

              2 log x × log x = log 10 + 2 log x

• Let log x = k, then:

              2k² = 2k + 1   .....(log 10 = 1)

              2k² - 2k - 1 = 0

• Now k = -b±√D / 2a

              k = 2±√4-4(2)(-1) / 4

              k = 2±√4+8 / 4

              k = 2±√12 / 4

              k = 2±2√3 / 4

              k = 1±√3/2

• So now re substituting the terms we get:

              log x =  1±√3/2

              x = e^1±√3/2

Answer:

           So the value of x is  e^1+√3/2 or  e^1-√3/2.

Answer 2

Answer Of Problem;

x = 10^1±√3/2

Logarithmic Properties Used-

• [loga(b)=n] → (aⁿ=b)..(1)

• loga(b)ⁿ = nloga(b)..(2)

•loga(m)+loga(n) = loga(mn)..(3)

Here Is Your Solution;

Taking Log Both The Sides-

log(x^2logx) = log10x²

2logx•logx = log(10•x²) ..[By (2)]

2logx•logx = log10+logx² ..[By (3)]

2logx•logx = 1 + 2logx. ..[By (2)]

Let logx=a, then

2a²=1+2a

2a²-2a-1=0

Using Quadratic Formula;

x= (-b±√b²-4ac)/2a

x=[-(-2)±√(-2)²-4(2)(-1)]/2(2)

x=[2±√12]/4

x=[1±√3]/2

logx= (1±√3)/2

Therefore, [x= 10^(1±√3)/2]

Thanku For Viewing!

Hope It Helps!