Math Snap

STEP 1

Assumptions1. The logarithm is in base10.
. The variables A, B, C, and D represent real numbers.

STEP 2

We can use the properties of logarithms to simplify the given expression. The first property we will use is the quotient rule, which states that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator.
$$\log \frac{B^{A}}{^{C}} = \log B^{A} - \log D^{C}$$

STEP 3

Next, we use the power rule of logarithms, which states that the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the number.
$$\log B^{A} - \log D^{C} = A \log B - C \log D$$

Now, we compare this expression with the given options. The expression $A \log B - C \log D$ matches with option G.
So, $\log \frac{B^{A}}{^{C}}$ is equal to $A \log B - C \log D$.