Questions: Convert to a logarithmic equation 216^(1/3)=6

Solution Steps

To convert the given exponential equation to a logarithmic equation, we need to use the property of logarithms that states \( a^b = c \) can be rewritten as \( \log_a(c) = b \). Here, \( a = 216 \), \( b = \frac{1}{3} \), and \( c = 6 \).

We start with the exponential equation: \[ 216^{\frac{1}{3}} = 6 \] To convert this to logarithmic form, we use the property that \( a^b = c \) can be rewritten as \( \log_a(c) = b \).

In our case:

• \( a = 216 \)
• \( b = \frac{1}{3} \)
• \( c = 6 \)

Thus, we can express the equation in logarithmic form as: \[ \log_{216}(6) = \frac{1}{3} \]

Final Answer