Logarithm of a Product
How to solve the logarithm of a product (loga xy): formula, 1 example, and its solution.
Formula
loga xy = loga x + loga y
You can split the log of a product like this.
Examplelog2 3 = a, log2 24 = ?
Solution
Solution (Detail)
Write the prime factorization of 24.
24 = 23⋅3
log2 23⋅3 = log2 23 + log2 3
log2 23 = 3 log2 2
Logarithm of a Power
log2 3 = a
So
log2 23 + log2 3
= 3 log2 2 + a.
log2 2 = 1
Logarithm of Itself
3⋅1 + a = a + 3
So a + 3 is the answer.