Explanation:
The equation logbx = logax / logab is used to change the base of a logarithm. Let's break it down step by step:
1. logbx = logax / logab
In this equation, b is the new base we want to convert the logarithm to, while a is the base of the original logarithm.
2. logax / logab
The numerator logax represents the logarithm of x with base a. The denominator logab represents the logarithm of b with base a.
3. Example:
Let's say we have the logarithm log35 with base 5, and we want to convert it to base 2.
Using the equation logbx = logax / logab, we have:
log2(3) = log5(3) / log5(2)
To find the values of log5(3) and log5(2), we can use the change of base formula, which states that logax = logcx / logca.
Using the change of base formula, we can rewrite the equation as:
log2(3) = log(3) / log(2)
Now, using a calculator or logarithm table, we can find the values of log(3) and log(2) to be approximately 0.477 and 0.301, respectively.
So, log2(3) = 0.477 / 0.301 ≈ 1.5849
Therefore, log35 with base 5 is approximately equal to 1.5849 with base 2.
I hope this explanation helps! Let me know if you have any further questions.