Questions: Write the equation in its logarithmic form. 4^3=64

Solution Steps

To convert an exponential equation to its logarithmic form, we use the relationship between exponents and logarithms. The equation \( a^b = c \) can be rewritten in logarithmic form as \( \log_a(c) = b \). Applying this to the given equation \( 4^3 = 64 \), we identify \( a = 4 \), \( b = 3 \), and \( c = 64 \).

We start with the exponential equation given by: \[ 4^3 = 64 \]

To express this equation in logarithmic form, we use the relationship: \[ a^b = c \implies \log_a(c) = b \] Here, \( a = 4 \), \( b = 3 \), and \( c = 64 \). Thus, we can rewrite the equation as: \[ \log_4(64) = 3 \]

Final Answer