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Use the following to review for your test. Work the Practice Problems on a Separate sheet of paper!You need to know and be able to do the followingThings to rememberPractice ProblemsSolve exponential equations.Rewrite the bases so they are the same!Once the bases are equal the exponents must be equal.Set the exponents equal and solve!42x+1=82x25x-1=151-3x-1212215-664845Solve each exponential equation:00Solve each exponential equation:Write an exponential equation in log form & a log equation in exponential form.The most important thing to remember is ‘a log is just a power’ It makes logs less intimidatinglog28=3What is the exponent needed on 2 to get the result 8?The base in the exponential equation is the same as the base in log form. The log equation is always equal to the “exponent” in the exponential form!30=1-29210-524510Write the exponential equation as a log equation:00Write the exponential equation as a log equation:13-3=27-64770-595630Write the log equation as an exponential equation:00Write the log equation as an exponential equation:-32385-45720Write the exponential equation as a log equation:00Write the exponential equation as a log equation:25-32=1125-53340-50165Write the log equation as an exponential equation:00Write the log equation as an exponential equation:log41=0log273=13-44450-687705Write the log equation as an exponential equation:00Write the log equation as an exponential equation:-37465-447675Write the log equation as an exponential equation:00Write the log equation as an exponential equation: log5125=-2Evaluate logs.Rewrite each term in exponential form and determine the power!145923023495Evaluate:00Evaluate:log327+log2165?log101-2?log1010log42+log864log343Know the Properties (Laws) of Logs!Use the properties of logs to expand and condense log expressions and equations.-35560-2689860a. logbb=1b. logb1=0c. logbbx=xd. blogbx=xe. logbM?N=logbM+logbNg. logbMN=logbM-logbNf. logbMx=x?logbMh. logbx1=logbx2iff x1= x200a. logbb=1b. logb1=0c. logbbx=xd. blogbx=xe. logbM?N=logbM+logbNg. logbMN=logbM-logbNf. logbMx=x?logbMh. logbx1=logbx2iff x1= x2-53340-16510Write each as a single log with a coefficient of 1 (condensed form)00Write each as a single log with a coefficient of 1 (condensed form)12log2a+log2b+log2c2log37+5log3a-log314a-2540090170Write each log as a sum or difference of logs (expanded form)0Write each log as a sum or difference of logs (expanded form)log3alog53x4Solve log equations.If there is only one logarithm in the equation, then rewrite as an exponential and solve.If there are two logarithms (with the same base) in the equation, then set the results equal and solve.Check for extraneous solutions! 4826027305Solve the equation- remember to keep 4 decimal places throughout your work!00Solve the equation- remember to keep 4 decimal places throughout your work!log36x=323.2e3x=6 (solve graphically)log83x+7=log87x+4logx116=-23x=28log4x2+6=log45x7e2x+2.5=20 (solve graphically)log13127=xlog2x+8=logx-4Graph the inverse of exponential growth/decay.Analyze the graph.Use transformations to translate exponential growth/decay and the inverses. Remember to determine the inverse of a graph . . . switch the x and y coordinates and plot the new coordinates. Because the x and y coordinates are switched look carefully at how this effects the analysis! Graph each of the following and answer the questions:25209525018900y=3(2)xDomain: _______ Range: _______y-intercept: ______Asymptote: ______Growth or Decay?Initial Value: _________Growth/Decay Factor: __________16319524828500y=log2xDomain: _______ Range: _______x-intercept: ______ Asymptote: ______50990529083000y=12x-3Domain: _______ Range: _______y-intercept: ______Asymptote: ______Growth or Decay?Initial Value: _________Growth/Decay Factor: __________ 58293022733000 y=log2(x+3)(look at transformation from #27)Domain: _______ Range: _______x-intercept: ______ y-intercept: ______Asymptote: ______You deposit $500 in a bank account. Find the balance after 2 years for each of the following situations.The account pays 2.25% annual interest compounded monthly.The account pays 1.75% annual interest compounded quarterly.The account pays 3% annual interest compounded continuously. How many years would it take for the account to have a value of $1000 if it continues to compound continuously but at a rate of 4% annual interest?You buy a car for $31,500. The value of the car decreases by 12.5% each year. Write a model to give the value of the car after t years. Estimate when the car will have a value of $12,000. ................
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