if a > 0 , ( a  = 1 ) , b > 0 , ( b  = 1 ) such that a ( l o g a b ) x = b ( l o g b a ) x then x =

Mathematics - Basic maths Question with Solution | TestHub

MathematicsBasic mathsLogarithmEasy2 minQB

MathematicsEasysingle choice

if $a > 0, (a \neq = 1), b > 0, (b \neq = 1)$ such that $a^{(l o g_{a}^{b})^{x}} = b^{(l o g_{b}^{a})^{x}}$ then $x =$

Answer:

Solution:

Taking $lo g_{b}$ on both sides, we get:

$(lo g_{a}^{b})^{x} lo g_{b}^{a} = (lo g_{b}^{a})^{x}$

Therefore,

$(lo g_{a}^{b})^{x} = (lo g_{b}^{a})^{x - 1}$

This implies $1 - x = x$ , which gives $x = \frac{1}{2}$ .

Stream:JEESubject:MathematicsTopic:Basic mathsSubtopic:Logarithm

⏱ 2mℹ️ Source: QB

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