How do you multiply logs with the same base?

To multiply logs with the same base, you can use the logarithmic property that states:

log_b(x) + log_b(y) = log_b(xy)

Here’s how it works:

1. First, ensure that the logarithms you are multiplying share the same base. For example, if you have log₁₀(a) and log₁₀(b), they both have base 10.
2. According to the property mentioned, you can combine them by adding their logarithmic values together.
3. So, instead of multiplying log₁₀(a) and log₁₀(b), you can rewrite it as log₁₀(a * b).

For example, if you want to multiply log₁₀(2) and log₁₀(3), you’d rewrite it as:

log₁₀(2) + log₁₀(3) = log₁₀(2 * 3) = log₁₀(6)

This property helps simplify logarithmic expressions and is particularly useful in solving logarithmic equations.