Number of real solutions of the equation √ log 10(-x)= log 10 √x2 is

Question

Number of real solutions of the equation √ log 10(-x)= log 10 √x2 is (A) none (B) exactly 1 (C) exactly 2 (D) 4

Tardigrade Admin · Accepted Answer

x <0 ; √ log 10(- x )= log 10| x | text squaring log 10(- x )= log 10 2(- x ) log 10(- x )=0 text or log 10(- x )=1 x =-1 text or x =-10] | x |=- x ; text for x <0

Q. Number of real solutions of the equation $lo g_{10} (- x) = lo g_{10} x^{2}$ is

none

exactly 1

exactly 2

4

$x < 0; lo g_{10} (- x) = lo g_{10} ∣ x ∣$
$squaring lo g_{10} (- x) = lo g_{10}^{2} (- x)$
$lo g_{10} (- x) = 0 or lo g_{10} (- x) = 1$
$x = - 1 or x = - 10]$
$∣ x ∣ = - x; for x < 0$

Q. Number of real solutions of the equation log10​(−x)​=log10​x2​ is

none

exactly 1

exactly 2

4

x<0;log10​(−x)​=log10​∣x∣ squaring log10​(−x)=log10​2(−x) log10​(−x)=0 or log10​(−x)=1 x=−1 or x=−10] ∣x∣=−x; for x<0

Q. Number of real solutions of the equation $lo g_{10} (- x) = lo g_{10} x^{2}$ is

$x < 0; lo g_{10} (- x) = lo g_{10} ∣ x ∣$
$squaring lo g_{10} (- x) = lo g_{10}^{2} (- x)$
$lo g_{10} (- x) = 0 or lo g_{10} (- x) = 1$
$x = - 1 or x = - 10]$
$∣ x ∣ = - x; for x < 0$