Questions: Change each equation to its equivalent logarithmic form. (a) 9^(4z) = 4 (b) e^z = 6 (c) c^Z = f (a) Find the equivalent equation for 9^(4z) = 4.

Solution Steps

To convert an exponential equation to its equivalent logarithmic form, we use the property that if \( a^b = c \), then the equivalent logarithmic form is \( \log_a(c) = b \). We will apply this property to each of the given equations.

Using the property of logarithms, we can rewrite the equation \( 9^{4z} = 4 \) in logarithmic form as follows: \[ \log_{9}(4) = 4z \]

For the equation \( e^{z} = 6 \), we apply the same logarithmic property: \[ \log_{e}(6) = z \] This can also be expressed as: \[ z = \ln(6) \]

Finally, for the equation \( c^{Z} = f \), we convert it to logarithmic form: \[ \log_{c}(f) = Z \]

Final Answer