Question

If \( 2 \log 5 + \frac{1}{2} \log 9 - \log 3 = \log x \), then the value of \( x \) is:

• A. \(42\)
• B. \(25\)
• C. \(52\)
• D. \(24\)

Hint:

For logarithmic equations, use the properties of logarithms to combine terms. Remember, \( \log a + \log b = \log(ab) \) and \( \log a - \log b = \log\left(\frac{a}{b}\right) \).

Answer 1

The Correct Option is B

We are given: \[ 2 \log 5 + \frac{1}{2} \log 9 - \log 3 = \log x \] Step 1: Simplify the logarithmic terms.
The first term can be simplified as: \[ 2 \log 5 = \log 5^2 = \log 25 \] The second term simplifies as:
\[ \frac{1}{2} \log 9 = \log 9^{1/2} = \log 3 \] The third term is already \( \log 3 \).
Thus, the equation becomes: \[ \log 25 + \log 3 - \log 3 = \log x \] Step 2: Simplify further.
Since \( \log 3 - \log 3 = 0 \), we have: \[ \log 25 = \log x \] Step 3: Equate the terms.
Since \( \log 25 = \log x \), it follows that: \[ x = 25 \]