Question

ANSWER :=:=.....................................................

Answer 1

★ LOGARITHMIC REDUCTIONS ★

Given that ;

☣ ( x√x ) ^x = ( x )^ x√x

By reducing the equivalents by taking logarithms on both the side -

☣ ( x√x ) ^x = ( x ) ^ x√x

☣ log ( x√x ) ^x = log ( x^x√x)

☣ x log ( x√x ) = x√x log ( x )

☣ x log ( x^3/2) = x√x log ( x )

☣ 3x/2 log ( x ) = x√x log ( x )

☣ 3x log ( x ) = 2x√x log ( x )

☣ 2x√x log ( x ) - 3x log ( x ) = 0

☣ x log ( x ) [ 2√x - 3 ] = 0

for the above relationship to be satisfied ,

either , x = 0 , log ( x ) = 0 , 2√x - 3 = 0

x ≠ 0 , because 0⁰ is indeterminate format
aslike , x log ( x ) = log ( x )^x , and violating logarithmic domain too

☣ log ( x ) = 0 , for sure x = 1

and if 2√x - 3 = 0 , then for sure , x = 9/4

Hence , the possible real numbers are x = 1 , 9/4

Option B is correct for above all results

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