Exponential and Logarithmic Functions

Question

The demand equation for a consumer product is q = 80 - 2^p. Solve for p and express your answer in terms of common logarithms. Evaluate p to two decimal places when q = 60.

Answer 1

q = 80 - 2^p

 

2^p = 80 - q

 

log(2^p) = log(80-q)

 

plog2 = log(80-q)

 

p = log(80-q)/log2

 

when q = 60, p = log20/log2 ≈ 4.32

 

 

Answer 2

q = 80 - 2^p

log q = log 80 - p log 2

p log2= log 80-log q

p= (log80 -log q)/ (log 2)

 

When q=60, p = (log80-log60) / log2 =0.41