Theory question 101
Logarithms(a) If (y − 1) log104 = y log1016, without using mathematical tables or calculator, find the value of y.
(b) When I walk from my house at 4 Km/h, I will get to the office 30 minutes later than when I walk at 5 km/h. Calculate the distance between my house and office.
Show the model answer
Model answer
(a) log 16 = log 4² = 2 log 4
(y − 1) log 4 = 2y log 4 → y − 1 = 2y → y = −1
(b) Let the distance be d km: d/4 − d/5 = ½
d/20 = ½ → d = 10 km
Explanation
Write log 16 as 2 log 4 and divide both sides by log 4.