Exciting Math Problem Solving with Logarithmic Properties

How can we use logarithmic properties to solve equations?

Let's solve the following equation: log₃ 5x + log₃ 7 = 4. Leave your answer in fraction form, please.

Solution:

Adding logs of the same base is equivalent to multiplying the arguments. You get:

When we have log₃ 5x + log₃ 7 = 4, we can combine the logs using logarithmic properties. This results in log₃ (5x * 7) = 4.

Next, we use the definition of logarithms to rewrite this equation as an exponential function: 3⁴ = 35x.

Solving for x, we find x = 81/35.

By understanding logarithmic properties, we can easily solve complex equations and enjoy the process of problem-solving in mathematics!