Examples Natural Logarithms – Example 1: Natural Logarithms – Example 2: Natural Logarithms – Example 3: Natural Logarithms – Example 4: Exercises for Natural Logarithms Find the value of \(x\) in each equation. \(\color{blue}{e^x=3,x=}\) \(\color{blue}{ln(3x-1)=1,x=}\) \(\color{blue}{lnx=9,x=}\) \(\color{blue}{e^x=9,x=}\) \(\color{blue}{ln(lnx )=2,x=}\) \(\color{blue}{ln(2x+4)=1,x=}\) \(\color{blue}{ln(3)}\) \(\color{blue}{\frac{e+1}{3}}\) \(\color{blue}{e^9}\) \(\color{blue}{2ln(3)}\) \(\color{blue}{e^{e^2}}\) \(\color{blue}{\frac{e-4}{2}}\)
Rationalizing Radical Expressions – Example 2: Rationalizing Radical Expressions – Example 3: Rationalizing Radical Expressions – Example 4: Exercises for Rationalizing Radical Expressions \(\color{blue}{\frac{15}{\sqrt{5}-2}}\) \(\color{blue}{\frac{\sqrt{3}+\sqrt{6}}{6-\sqrt{5}}}\) \(\color{blue}{\frac{4+\sqrt{2}}{\sqrt{2}-\sqrt{7}}}\) \(\color{blue}{\frac{2+\sqrt{8}}{\sqrt{3}-\sqrt{2}}}\) \(\color{blue}{\frac{\sqrt{9c}}{\sqrt{c^5}}}\) \(\color{blue}{\frac{10}{7-\sqrt{6}}}\) \(\color{blue}{15(\sqrt{5}+2)}\) \(\color{blue}{\frac{(\sqrt{3}+\sqrt{6})(6+\sqrt{5})}{31}}\) \(\color{blue}{-\frac{4\sqrt{2}+4\sqrt{7}+2+\sqrt{14}}{5}}\) \(\color{blue}{2\sqrt{3}+2\sqrt{2}+2\sqrt{6}+4}\) \(\color{blue}{\frac{3}{c^2}}\) \(\color{blue}{\frac{10(7+\sqrt{6})}{43}}\)
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