The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

If we encounter two logarithms with the same base, we can likely combine them. In this case, we can use the reverse of the above identity.

Use the rule:

therefore

When adding logarithms of the same base, all you have to do is multiply the numbers inside the function as shown below:

The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

If we encounter two logarithms with the same base, we can likely combine them. In this case, we can use the reverse of the above identity.

The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.

If we encounter two logarithms with the same base, we can likely combine them. In this case, we can use the reverse of the above identity.

Use the rule:

therefore

When adding logarithms of the same base, all you have to do is multiply the numbers inside the function as shown below:

According to log rules, the coefficients of the logs can be raised as powers for the inner quantity of the log. Rewrite the terms.

Subtract the .

The answer is:

A statement can be proved to not be true in general if one counterexample can be found. One such counterexample assumes that . The statement

becomes

or, equivalently,

The word "log" indicates a common, or base ten, logarithm, as opposed to a natural, or base , logarithm. By definition, the above statement is true if and only if

,

or

.

This is false, so does not hold for . Since the statement fails for one value, it fails in general.

By the Change of Base Property of Logarithms, if and ,

Substituting 7 for and 6 for , the statement becomes the given statement

.

The correct choice is "true."