example of log rulesy frac12 gt2 where g

Question

Example of Log Rules:

Y = ½ gt² where g = 32

Solution:

y = 16 t²

Find y for t = 10 using logs.

log y = log₁₀    (16 t²)

log₁₀y = log₁₀ 16 + log₁₀ t²

log₁₀y = log₁₀ 16 + (2 log₁₀ t)

log₁₀y = 1.204 + 2 log₁₀ 10

log₁₀y = 1.204 + 2 x 1

log₁₀y = 3.204

but this means 10^3.204  = y

y = 1600