The problem asks to express $log(8) + log(10) - log(2)$ as the logarithm of a product or quotient.

AlgebraLogarithmsLogarithm Properties
2025/4/10

1. Problem Description

The problem asks to express log(8)+log(10)log(2)log(8) + log(10) - log(2) as the logarithm of a product or quotient.

2. Solution Steps

We can use the logarithm properties to simplify the expression.
log(a)+log(b)=log(ab)log(a) + log(b) = log(a * b)
log(a)log(b)=log(a/b)log(a) - log(b) = log(a / b)
Using these properties, we can rewrite the expression as:
log(8)+log(10)log(2)=log(810)log(2)log(8) + log(10) - log(2) = log(8 * 10) - log(2)
log(810)log(2)=log(80)log(2)log(8 * 10) - log(2) = log(80) - log(2)
log(80)log(2)=log(80/2)log(80) - log(2) = log(80 / 2)
log(80/2)=log(40)log(80 / 2) = log(40)

3. Final Answer

log 40