Question

Expand the logarithmic expression

Answer 1

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)

Answer 2

Answer:

 $\frac{1}{2}log13-\frac{1}{2}log74$ is the expansion of the given logarithmic function.

Step-by-step explanation:

We have been given an expression:

$log_b\sqrt{\frac{13}{74}}$

Since, we know $\sqrt{x}=x^\frac{1}{2}$

The given expression can be rewritten as:

$log_b(\frac{13}{74})^\frac{1}{2}$

Now, using logarithmic property:

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

$\frac{1}{2}log_b\frac{13}{74}$

Now, using $log\frac{m}{n}=logm-logn$

Here, m=13 and n=74

$\frac{1}{2}log13-\frac{1}{2}log74$ is the expansion of the given logarithmic function.