Question

Condene the expression log3x log34 to the logarithm f a single term

A. \(\log₃(x ⋅ 34)\)
B. \(\log₃(34x)\)
C. \(\log₃\left(\frac{x}{34}\right)\)
D. \(\log₃(x + 34)\)

Answer 1

To condense log3x log34 into a single logarithm, we apply the rule that the logarithm of a product is the sum of the logarithms. Thus, the condensed form is log3(34x), which is option B.

Step-by-step explanation:

The expression log3x log34 seems to be the product of two logarithms and it suggests that we need to condense them into a single logarithm. To do this, we use a rule of exponents that says the logarithm of a product of two numbers equals the sum of their logarithms, i.e., log(xy) = log x + log y.

Given our expression log3x log34, we can combine these following this rule and state:

log3x + log34 = log3(x · 34)

So, applying this rule gives us the equivalent expression, which is log3(34x). This corresponds to option B.