Answer:
b = 6.79
Step-by-step explanation:
Data provided:
logb(5) = 0.84
Now,
From the properties of log function
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)
thus,
using the above properties, we can deduce the results as:
logₓ(y) = n is equivalent to y = xⁿ
Thus,
logb(5) = 0.84
⇒ [tex]\frac{\log(5)}{\log(b)}[/tex] = 0.84
or
log(5) = 0.84 × log(b)
or
log(5) = [tex]\log(b^{0.84})[/tex] (as log(xⁿ) = n × log(x) )
taking the anti-log both sides
we get
5 = [tex]b^{0.84}[/tex]
or
b = 6.79
