[Step 9: Logarithm Calculation Practice: Let's Combine the 3 Formulas Learned So Far] Understanding Logarithms in 1 Minute: 20-Part Series for Overwhelming Knowledge
Hello, this is KoTa.
Even calculations that look complex at first glance can always be solved by applying the rules we've learned so far in order. Let's simplify the following expression into a single number.
log_2 12 + log_2 6 - log_2 9
Let's take it one step at a time.
First, turn addition into 'multiplication' log_2 (12 × 6) - log_2 9 = log_2 72 - log_2 9
Next, turn subtraction into 'division' log_2 (72 / 9) = log_2 8
Finally, think about 'what power' To what power must 2 be raised to get 8? The answer is 3!
How was that? The separate 'log' terms transformed into a single number, '3', at the end. In this way, 'combining them first and then thinking about the exponential form at the end' is the smart way to solve problems without making calculation errors.
Key points for this lesson
Apply the rules in order from left to right.
Addition means 'multiplication of the contents,' and subtraction means 'division of the contents.'
Finally, check 'to what power the base must be raised to get the antilogarithm' to finish!
What's the next step?
Step 10: Change of Base Formula (1): The Savior When Bases Are Different
Up until now, the 'bases' have all been the same (e.g., all log_2). But what if you encounter an expression where the 'bases are different'...? I will teach you the most famous 'change of base formula' in the world of logarithms, which breaks through such desperate situations!
See you then!