Simplify each expression using any needed combination of logarithm identities.
1. \(\ln(4e)\)
2. \(\ln(8e^3)\)
3. \(\ln(12) + ln(16) - \ln(4)\)
4. \(\log_{10}(200)\)
5. \(4\ln(2) + 3\ln(5)\)
6. \(\log_{2}(9)\log_{9}(4)\)
Simplify each expression using a combination of exponent laws and logarithm identities.
7. \(8^{\log_{8}(2)}\)
8. \(e^{4\ln(2)}\)
9. \(4^{\log_{2}(5)}\)
10. \(9^{\log_{3}(7)} \cdot 3^{\log_{3}(2)}\)
11. \(\log_{6}(36^7 \cdot 6^2)\)
12. \(5\log_{12}(2) + 2\log_{144}(4)\)