To solve the logarithmic equation [tex]\(\log_z 4 = 6\)[/tex], we need to understand what this logarithmic statement translates to in its exponential form.
The equation [tex]\(\log_z 4 = 6\)[/tex] means that [tex]\(z\)[/tex], raised to the power of 6, equals 4. This is based on the definition of logarithms where if [tex]\(\log_b a = c\)[/tex], then [tex]\(b^c = a\)[/tex].
Here, [tex]\(b\)[/tex] is [tex]\(z\)[/tex], [tex]\(a\)[/tex] is 4, and [tex]\(c\)[/tex] is 6. So, we translate [tex]\(\log_z 4 = 6\)[/tex] to its exponential form:
[tex]\[ z^6 = 4 \][/tex]
Thus, the correct answer is:
[tex]\[ z^6 = 4 \][/tex]
