# Exponents and logarithms

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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?

Suppose that $2000 is invested at a rate of 6% per year compounded continuously. What is the balance after 1 yr? After 2 yrs?

For part E(a), the question actually involves x being an exponent. You need to worked with it as 2x to the power of x.

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This shows how to solve logarithmic equations and convert between logarithmic and exponential forms.

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