Solving Exponential Equations Math Example 2

Solution

1. 1
   Take the natural logarithm of both sides: $\ln(5^{2x-1}) = \ln(12)$.
2. 2
   Apply the power rule: $(2x-1)\ln(5) = \ln(12)$.
3. 3
   Solve for $x$: $2x - 1 = \frac{\ln(12)}{\ln(5)}$, so $2x = \frac{\ln(12)}{\ln(5)} + 1$.
4. 4
   $x = \frac{1}{2}\left(\frac{\ln 12}{\ln 5} + 1\right) = \frac{1}{2}\left(\frac{2.4849}{1.6094} + 1\right) \approx \frac{1}{2}(1.5440 + 1) \approx 1.272$.