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!