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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?1lnx1e1xeonesolutionatx2.21910715logx=log10x?1logx1110c10threesolutionsx12.69625656x27.32834778x38.26382974

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