Step by step
The question
Question: write log₂ x + log₂ y as one log.
log2 x + log2 y
The three log rules, used backwards.
A number in front goes up as a power.
Plus becomes times.
Minus becomes divide.
n × log a = log(an)
log a + log b = log(a × b)
log a − log b = log(ab)
1 Plus becomes times
Plus between logs becomes times inside: x and y multiplied.
log a + log b = log(a × b)
So it is one log: log₂(xy).
= log2(xy)
2 Check
Let's check with numbers: x = 3, y = 2.
With a calculator, the question is about 2.585.
x = 3, y = 2: question ≈ 2.585
Our answer: the inside is 6, and its log is about 2.585.
The same.
It works!
answer: log2 6 ≈ 2.585
Let's look back.
First: plus becomes times.
Last: check.
Answer
= log2(xy)