Question

If \(\log_{a^{4}}65536=2\), what is the value of 'a'?

• A. 2
• B. 4
• C. 6
• D. 8
• E. √2

Answer 1

The Correct Option is B

To solve the problem \(\log_{a^{4}}65536=2\), we want to find the value of 'a'.

First, understand the logarithmic equation:

\(\log_{a^{4}}65536=2\) implies that \((a^{4})^{2} = 65536\).

This is because if \(\log_{b}c = d\), then \(b^{d} = c\).

Thus, we have:

\(a^{8} = 65536\).

Next, express 65536 as a power of 2:

\(65536 = 2^{16}\).

The equation becomes:

\(a^8 = 2^{16}\).

Equate the exponents:

This gives \(a = 2^{2}\) because \(a^{8} = 2^{16}\) implies \(a = 2^{16/8} = 2^{2}\).

Therefore, the value of 'a' is 4.

The correct answer is 4, as derived from the calculation.