Question

The value of \(\text{log}_{625}\ 5\) is

• A. \(\frac{1}{2}\)
• B. \(\frac{1}{4}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{1}{5}\)

Answer 1

The Correct Option is B

Step 1: Express 625 as a power of 5 We know that \[ 625 = 5^4 \] Step 2: Use change of base identity \[ \log_{625} 5 = \log_{5^4} 5 \] Using the identity \(\log_{a^m} b = \frac{1}{m} \log_a b\), we get \[ \log_{5^4} 5 = \frac{1}{4} \log_5 5 \] Step 3: Simplify further \[ \log_5 5 = 1 \] So, \[ \log_{625} 5 = \frac{1}{4} \]

The correct option is (B): \(\frac{1}{4}\)