Consider the equation 2^2/3=100

Question

Solve the equation by using the logarithm base 10. Then solve by using the logarithim base 2.

Compare your solutions. What are the advantages of each method? Explain.

Answer 1

Assuming you meant to write:

2^2x/3 = 100

Using log base 10 (written as just log) and noting that 100 = 10²:

log(2^2x/3) = log(10²)

Use the log property log(a^b) = b log(a) and log_a(a) = 1::

2x/3 log(2) = 2

x = 3/log(2)

Using log base 2 (log₂):

log₂(2^2x/3) = log₂(10²)

2x/3 = 2 log₂(10)

x = 3 log₂(10)

Use your calculator to verify that 3/log(2) = 3 log₂(10). Or you can verify it using the change of log base formula.