Find the solution of the exponential equation \( 14^{-\frac{z}{7}}=18 \) in terms of logarithms, or correct to four decimal places. \( x=\square \)

To solve the equation \( 14^{-\frac{z}{7}}=18 \), we can use logarithms. First, take the natural logarithm of both sides: \[ -\frac{z}{7} \ln(14) = \ln(18) \] Now, isolate \( z \): \[ -\frac{z}{7} = \frac{\ln(18)}{\ln(14)} \] Multiplying both sides by -7 gives: \[ z = -7 \cdot \frac{\ln(18)}{\ln(14)} \] Calculating this gives: \[ z \approx -7 \cdot \frac{2.8904}{2.6391} \approx -7 \cdot 1.095 = -7.665 \] Thus, correct to four decimal places, \( z \approx -7.6650 \).