Question

Extension: Suppose that there is some positive number bb so that logb(5) = 0.84.

Answer 1

Answer:

b = 6.79

Step-by-step explanation:

Data provided:

logb(5) = 0.84

Now,

From the properties of log function

logₓ (z)= $\frac{\log(z)}{\log(x)}$  (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

⇒ $\frac{\log(5)}{\log(b)}$ = 0.84

or

log(5) = 0.84 × log(b)

or

log(5) = $\log(b^{0.84})$                (as log(xⁿ) = n × log(x) )

taking the anti-log both sides

we get

5 = $b^{0.84}$

or

b = 6.79