Find the solution of the exponential equation \( 8^{-\frac{x}{14}}=6 \) in terms of logarithms, or correct to four decimal places. \( x= \) Ouestion 3

To solve the equation \( 8^{-\frac{x}{14}}=6 \), we start by taking the logarithm of both sides. This gives us: \[ -\frac{x}{14} \cdot \log(8) = \log(6) \] Now, we can isolate \( x \): \[ x = -14 \cdot \frac{\log(6)}{\log(8)} \] Using a calculator, we find: \[ \log(6) \approx 0.7781 \quad \text{and} \quad \log(8) \approx 0.9031 \] Plugging in these values: \[ x \approx -14 \cdot \frac{0.7781}{0.9031} \approx -14 \cdot 0.8617 \approx -12.0838 \] Thus, rounded to four decimal places, the solution is: \[ x \approx -12.0838 \]