Question

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

Answer 1

b = 6.79

Explanation:

Data provided:

logb(5) = 0.84

Now,

From the properties of log function

logₓ (z)=
`(\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

⇒
`(\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