Converting to Exponential & Logarithmic Functions
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A. Convert to logarithmic equations. For example, the logarithmic form of "23 = 8" is "log2 8 = 3".
a) 16 3/2 = 64
b) ex = 5
B. Write the logarithmic equation in exponential form. For example, the exponential form of "log5 25 = 2" is "52 = 25".
a) log 3 27 = 3
b) log e 1 = 0
c) log 125 25 = 2/3
C. Use the properties of logarithmic functions to expand the following logarithmic expressions
a) log10 4x2y
b) log a [(7x + 4)1/2 / 3]
D. Express the following as a single logarithm.
a) ½ log 10 x + 2 log 10 ( x - 2)
b) 4 log 10 (x - 3) - log 10 x
E. Solve the following for x:
a) 4(2x) = 56
b) ex = 66
c) ex - 5 = 41
d) log10 5x + log10 (x + 1) = 2
e) 2 log5 9x = 6
F. When interest is compounded continuously, the balance in an account after t years is given by A = Pert,
Where P is the initial investment and r is the interest rate.
Use the formula given to solve the following:
a) Maya has deposited $600 in an account that pays 5.64% interest, compounded continuously. How long will it take for her money to double?
b) Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?
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Solution Summary
Exponential and logarithmic functions are fully investigated in the attached Word document.
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