Answer:
[tex]-\frac{1}{\log(x)} [/tex]
Step-by-step explanation:
Data provided:
logₓ (1/10)
Now,
From the properties of log function
[tex]\log\frac{A}{B}[/tex] = log(A) - log(B)
logₓ (z)= [tex]\frac{\log(z)}{\log(x)}[/tex] (where the base of the log is equal for both numerator and the denominator)
also,
log(xⁿ) = n × log(x)
Therefore,
logₓ (1/10) = logₓ(1) - logₓ(10)
= [tex]\frac{\log(1)}{\log(x)} - \frac{\log(10)}{\log(x)}[/tex] (here log = log₁₀)
= [tex]\frac{0}{\log(x)} - \frac{\log(10)}{\log(x)}[/tex] (as log(1) = 0)
= [tex]-\frac{\log(10)}{\log(x)}[/tex]
= [tex]-\frac{1}{\log(x)}[/tex] (as log(10) = 1)
Therefore,
the given equation can be rewritten as [tex]-\frac{1}{\log(x)}[/tex]
