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Assignment 7B: Solving Exponential & Logarithmic Equations Total: 38 marks Show your work for full marks. Reminder: You're welcome to use Desmos to verify your answers. 1. Solve each equation. [6 marks] a) log2(2x10) =5 b} log3(x23x+5) =5 2. Solve for x. [6 marks] a) lognx + log11(x + 1) = log\" 6 b} log2(x + 7) log2(2x) = 3 3. 4. Solve for x. [6 marks] a) logx3 log2 = log(2x2) b} log(x + 5) 1 = log(x + 1) A 52500 investment earns 8% interest, compounded quarterly {4 times a year}. [6 marks] a) Write an equation for the value of the investment as a function of time, V(t), with t in years. b) How long will it take for the investment to be worth $4000? c} Change the base of the power so its exponent is just "t". 5. A bacteria culture starts with 3000 bacteria and grows to 50,000 in 3 hours. [5 marks] a) What is the doubling time (the time it takes for the bacteria to double in number)? b) How long will it take to reach 200,000 bacteria? A 50 mg sample of thorium-233 decays to 44 mg after 4 min. [5 marks] a) Determine the half-life of tho rium-233. b) How long will it take for this sample to decay to 1 mg? Given that 3 : J + i , determine the exact value of m + i [4 marks]