Questions: Convert log base 4 of 16 equals 2 to exponential form.

Solution Steps

To convert a logarithmic equation to its exponential form, we use the property that if \(\log_b(a) = c\), then \(b^c = a\). In this case, \(\log_4(16) = 2\) can be rewritten in exponential form as \(4^2 = 16\).

We start with the logarithmic equation \( \log_4(16) = 2 \). To convert this to exponential form, we use the property that if \( \log_b(a) = c \), then \( b^c = a \). Here, we have: \[ 4^2 = 16 \]

Next, we calculate \( 4^2 \): \[ 4^2 = 16 \] This confirms that the exponential form is correct since both sides of the equation are equal.

Now, we compare our result \( 4^2 = 16 \) with the provided options:

• A. \( 16^2 = 4 \)
• B. \( 4^2 = 16 \) (This matches our result)
• C. \( 4^{16} = 2 \)
• D. \( 2^{16} = 4 \)
• E. \( 2^4 = 16 \)
• F. None of the above

The correct option is B.

Final Answer