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Question Number 206177 by MATHEMATICSAM last updated on 08/Apr/24
Find total number of solutions of the equation sinx = logx.
Findtotalnumberofsolutionsoftheequationsinx=logx.
Answered by Frix last updated on 08/Apr/24
log x =ln x ? −1≤ln x ≤1 ⇔ e^(−1) ≤x≤e ⇒ one solution at x≈2.21910715 log x =log_(10) x ? −1≤log x ≤1 ⇔ (1/(10))≤c≤10 ⇒ three solutions x_1 ≈2.69625656 x_2 ≈7.32834778 x_3 ≈8.26382974
logx=lnx?−1⩽lnx⩽1⇔e−1⩽x⩽e⇒onesolutionatx≈2.21910715logx=log10x?−1⩽logx⩽1⇔110⩽c⩽10⇒threesolutionsx1≈2.69625656x2≈7.32834778x3≈8.26382974

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