Do question 11 please Write log ((w + 4)^3/squareroot z^5) as the sum, differenc

Question

Do question 11 please

Write log ((w + 4)^3/squareroot z^5) as the sum, difference and/or multiple of logs. b) use your calculator to find log_15(345678) to 4 decimal places _____ c) Find the inverse function for f(x) = log_4(x-3) _____ Solve the logarithmic equation. Provide all of the solutions rounded to one decimal place and check. log_2(x - 7 + log_2(x) = 3) Find all real solutions, x, to 3 decimal places: e^2x - e^x = 6 Suppose $6000 is in a saving account paying an annual interest rate of r% 10 suppose compounded continuously. If the amount in the account after 30 years is $48000, find the annual percent rate rounded off to the nearest 1/10%. (Use A = Pe^rt here) How much must be invested at 6% per year compounded monthly, so that after 30 years it would be worth $40,000 (Use A = P(1 + r/n)^nt here)

Explanation / Answer

9) let e^x = t

Therefore equation is t^2 - t - 6 = 0

=> t^2 -3t +2t -6 =0

=> t (t-3) +2(t-3) = 0

=> (t-3) (t+2) = 0

=> t = 3 or -2

=> e^x = 3 or -2

But e^x can not be negative

=> e^x = 3

=> x = ln 3 = 1.0986 = 1.099

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