MODERATE EXERCISES - Logarithms and Solving Equations

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(1) Simplify.

1. ln
   
   
2. ln e^2x
   
   
3. e^{ln 3}

( Click On HINT To Get Some Help , Click On SOLUTION To See The Answers )

(2) Express without e or ln: e^{t ln 2} .

( HINT , SOLUTION )

(3) Rewrite so there are no logarithms of products, powers or quotients.

1. ln (x³ e^x)
   
   
2. log (sin x ) / (x+4)

( HINT , SOLUTION )

(4) Solve each equation.

1. 100 = 50e^-x
   
   
2. 1/4 = 5^2t-1
   
   
3. ln (2x+5) = 0
   
   
4. log_x 6 = 1/3

( HINT , SOLUTION )

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