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Some logarithmic problems are solved by simply dropping the logarithms while others are solved by rewriting the logarithmic problem in exponential form. How do we decide what is the correct way to solve a logarithmic problem?
(a) Find a formula for the number of bacteria at time t. (b) Find the number of bacteria after one hour. (c) After how many minutes will there be 50 000 bacteria?
Expand each logarithm. 1) ln (85 7) 4 2) ln (ca × b) 3) ln (uv6) 5 4) ln (x × y × z6) Condense each expression to a single logarithm. 5) 25ln5 - 5ln116) 5lnx + 6lny 7) ln5 2 + ln6 2 + ln7 2 8) 20lna - 4lnb Use a calculator to approximate each to the nearest thousandth. 9) ln39 10) ln2.2 11) ln21 12) ln3.4 Solve each equation.Round your final ...
Logarithmic Equations Date_____ Period____ Solve each equation. 1) log 5 x = log (2x + 9) {3} 2) log (10 − 4x) = log (10 − 3x) {0} 3) log (4p − 2) = log (−5p + 5) {7 9} 4) log (4k − 5) = log (2k − 1) {2} 5) log (−2a + 9) = log (7 − 4a) {−1} 6) 2log 7 −2r = 0 {− 1 2} 7) −10 + log 3 (n + 3) = −10 {−2} 8) −2log 5 7x ...
Solve each of the following logarithmic equations. a) log (2 7) log 2log 3a a ax x+ = + b) log (3 10) log 2log 3a a ay y+ − = c) log (2 1) 2 log2 2z z+ = + d) log (4 1) log ( 1) 23 3w w+ − − = e) log (3 4) log 32 2t t+ − = x =1 , 5 3 y = , 1 2 z = , w = 2 , 4 5 t =
-When solving a logarithmic equation, you want to make sure that you contract any logs on either side of the equation. -Once all logs are contracted, exponentiate to get rid of logs. -Solve the resulting algebraic equation. -Check for extraneous solutions. Example 1: Solve the following logarithmic equation. log( 2 − − 5) = 0. SOLUTION:
Solving Logarithmic Equations (Word Problems) Example 1. INVESTMENT Mr. and Mrs. Mitchell are saving for their daughter’s college education. They invest $10,000 in an account that pays 4.5% interest compounded continuously with the goal to have twice that amount in the account in ten years. a.
