a. What is the logarithmic form for 4 3 = 64 b. What is the value of log 2 (128)

Question

a. What is the logarithmic form for 43 = 64

b. What is the value of log2 (128)? Explain how you know.

Doctors monitoring the growth of tumor cells in a cancer patient know that the initial tumor cell count was 600 and that the cell growth is increasing at a rate of 22.5% per day.

a. Write an exponential function to model the number N of cancer cells t days after the initial reading.

b. Write the equivalent logarithmic function model. What do the independent and dependent variables in the model represent?
c. The type of treatment prescribed for the patient is determined by how fast the tumor cells are growing.
The doctors use 60,000 cells as their benchmark number. How many days after the initial cell count will this occur?

Explanation / Answer

a) We have 4^3 = 64

We know the relation:-

if y= b^x then we have log(base b) y = x

hence 4^3 = 64 hence we have log(base4)64 = 3

b) log (base2) 128

Using the above relation we have

log (base2) 128 = 7

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