Question

Which of the following is incorrect? Group of answer choices log(x)log(2) = log 2x log3 - log8 =log(3/8) log(ab) = loga + logb log(xyz) = logx + logy + logz

Answer 1

The incorrect statement is 'log(x)log(2) = log 2x'. This does not follow the logarithmic product property which states that the log of a product is the sum of the logs.

Step-by-step explanation:

The incorrect statement among the provided options is log(x)log(2) = log 2x. According to the properties of logarithms, specifically the product property, the logarithm of a product of two numbers is the sum of their logarithms (log(ab) = loga + logb). Additionally, the logarithm resulting from the division of two numbers is the difference between their logarithms (log(a/b) = loga - logb). Finally, the logarithm of a number raised to an exponent is the product of that exponent and the logarithm (log(a^b) = bloga).

The other statements provided are consistent with logarithmic properties:

• log3 - log8 = log(3/8)
• log(ab) = loga + logb
• log(xyz) = logx + logy + logz