Solve each equation.
$7^{y-3}=50$

Verified step by step guidance

1. First, recognize that the equation is in the form of an exponential equation: \( 7^{y-3} = 50 \). Our goal is to solve for \( y \).
2. To solve for \( y \), take the natural logarithm (ln) of both sides of the equation to bring down the exponent: \( \ln(7^{y-3}) = \ln(50) \).
3. Apply the logarithmic identity \( \ln(a^b) = b \cdot \ln(a) \) to the left side: \( (y-3) \cdot \ln(7) = \ln(50) \).
4. Isolate \( y-3 \) by dividing both sides by \( \ln(7) \): \( y-3 = \frac{\ln(50)}{\ln(7)} \).
5. Finally, solve for \( y \) by adding 3 to both sides: \( y = \frac{\ln(50)}{\ln(7)} + 3 \).