Question

Expand the logarithmic expression

logb square root of 13/74

1. 1/2 logb 13 - 1/2logb 73
2. 1/2 logb 13 + 1/2logb 73
3. logb (13-73)
4. sqrt logb (13-73)

Answer 1

`(1)/(2)log13-(1)/(2)log74` is the expansion of the given logarithmic function.

Explanation:

We have been given an expression:

`log_b\sqrt{(13)/(74)}`

Since, we know
`√(x)=x^(1)/(2)`

The given expression can be rewritten as:

`log_b((13)/(74))^(1)/(2)`

Now, using logarithmic property:

`log m^n=nlogm` so we get:

`(1)/(2)log_b(13)/(74)`

Now, using
`log(m)/(n)=logm-logn`

Here, m=13 and n=74

`(1)/(2)log13-(1)/(2)log74` is the expansion of the given logarithmic function.

Answer 2

The mathematical expression of the given above,
logb (13/74)^1/2
Distribute the exponent to both numerator and denominator.
logb (13^1/2 / 74^1/2)
To simplify, multiply the exponent to the expression and since it is division it may be expressed as difference of two logarithms.
(1/2)(logb 13) - (1/2)(log 74)