Math, asked by ANONYMOUS7799, 15 days ago

if x is the positive number that satisfies the equation log 2x2-21x+50 base 10= 2 then the value of 2x=?​

Answers

Answered by MaheswariS
4

\underline{\textbf{Given:}}

\mathsf{log\,_{10}(2x^2-21x+50)=2}

\underline{\textbf{To find:}}

\textsf{The value of 2x}

\underline{\textbf{Solution:}}

\mathsf{Consider,}

\mathsf{log\,_{10}(2x^2-21x+50)=2}

\textsf{Convert it into exponential form}

\mathsf{2x^2-21x+50=10^2}

\mathsf{2x^2-21x+50=100}

\mathsf{2x^2-21x-50=0}

\mathsf{2x^2-25x+4x-50=0}

\mathsf{x(2x-25)+2(2x-25)=0}

\mathsf{(x+2)(2x-25)=0}

\mathsf{x=-2,\dfrac{25}{2}}

\textsf{But x is a positive number}

\implies\boxed{\mathsf{x=\dfrac{25}{2}}}

\mathsf{2x=2\left(\dfrac{25}{2}\right)=25}

\therefore\mathsf{2x=25}

\underline{\textbf{Find more:}}

Log (6x^2-5x+1) base 1-2x - log (4x^2 -4x+1) base 1-3x = 2​

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