Question

If $\log_a b = 2$, then $b = ?$

• A. $a^2$
• B. $2a$
• C. $a/2$
• D. $\sqrt{a}$

Hint:

Just remember: The base of the log stays the base of the power. The number on the other side of the "=" is always the exponent.

Answer 1

The Correct Option is A

To solve the problem, we start with the given logarithmic equation:

\(\log_a b = 2\)

The logarithmic equation \(\log_a b = c\) is equivalent to the exponential form:

\(b = a^c\)

In this particular problem, \(c = 2\). Therefore, we can rewrite the equation as:

\(b = a^2\)

This tells us that \(b\) is equal to \(a\) raised to the power of 2. Among the options given:

• \(a^2\)
• \(2a\)
• \(\frac{a}{2}\)
• \(\sqrt{a}\)

The correct choice is \(a^2\), which matches the expression derived from the equation.

Conclusion: The value of \(b\) is \(a^2\).