Question

If log10x - log10√x = 2logx10, then the possible value of x is given by

Answer 1

Hope u got ur answer

if i didn't mistake

Answer 2

x = 100  or  1/100 if log₁₀x - log₁₀√x  = 2logₓ10

Step-by-step explanation:

log₁₀x - log₁₀√x  = 2logₓ10

=> log₁₀x - log₁₀(x)^(1/2)  = 2log₁₀10/log₁₀x

using logₐb   = logₓb/logₓa

=>  log₁₀x - (1/2) log₁₀x  = 2log₁₀10/log₁₀x

using log aⁿ  = n log a

=> 2log₁₀x -  log₁₀x  = 2* 2log₁₀10/log₁₀x

=> log₁₀x = 4 * 1 /log₁₀x

=> ( log₁₀x)² = 4

log₁₀x  = ±2

=> x = 10⁺²  or 10⁻²

=> x = 100  or  1/100

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