Solve the given equation for \( x \) \( 5^{4 x-4}=42 \) \( x=\square \) Question Help: \( \square \) Video

To solve the equation \( 5^{4x - 4} = 42 \), we begin by applying logarithms to both sides. Taking the natural logarithm (ln) or common logarithm (log) can help isolate the variable \( x \): 1. Apply the logarithm: \[ \log(5^{4x - 4}) = \log(42) \] 2. Use the power rule of logarithms: \[ (4x - 4) \cdot \log(5) = \log(42) \] 3. Now, divide both sides by \( \log(5) \): \[ 4x - 4 = \frac{\log(42)}{\log(5)} \] 4. Next, add 4 to both sides: \[ 4x = \frac{\log(42)}{\log(5)} + 4 \] 5. Finally, divide by 4 to find \( x \): \[ x = \frac{\frac{\log(42)}{\log(5)} + 4}{4} \] Simplifying this expression provides the solution for \( x \). Use a calculator to find the values of \( \log(42) \) and \( \log(5) \) for a numeric answer. Thus, the value of \( x \) is approximately: \[ x \approx 1.146 \]