Logarithms

Step 1: Understanding the equation.
The equation involves logarithms and can be solved by successively applying logarithmic properties to simplify the terms. After simplification, we find that .

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer:

Step 1: Use a calculator.
The cube root of can be calculated using a calculator.
Step 2: Conclusion.
Thus, the value of is .
Final Answer:

Step 1: Using logarithmic properties.
The sum of logarithms can be expressed as the logarithm of the product. Therefore, is equal to .

Step 2: Conclusion.
The correct answer is , corresponding to option (4).

Step 1: Recall the logarithmic identity
We are asked to find .
The logarithmic identity means that . In this case, means that .
Step 2: Express 32 as a power of 2
We know that: Thus, the equation becomes: Step 3: Solve for
Since the bases are the same, we can equate the exponents: Answer: Therefore, . So, the correct answer is option (1).