Скачать или смотреть Solving Logarithmic Equations | Step-by-step Guide|

Solving Logarithmic Equations | Step-by-step Guide|

Struggling with logarithmic equations? In this comprehensive tutorial, we'll guide you through solving logarithmic equations from beginner to advanced levels. Whether it's a simple equation like log_2 (x) = 4 or a more complex one involving multiple logs, we cover the essential strategies you need to know.

We break down the two main approaches: using the one-to-one property of logarithms and converting logs to their equivalent exponential form . You'll also learn how to use the product, quotient, and power rules to combine or expand log expressions to solve for x . Plus, we’ll show you how to check for extraneous solutions—a critical step to ensure your answer is valid .


Key Concepts Explained:

Definition of a Log: Remember, a logarithmic equation log_b (x) = y is equivalent to the exponential equation b^y = x. This is the foundation for solving many problems .

Logarithm Properties: We use the Product Rule (log_b (M) + log_b (N) = log_b (MN)), Quotient Rule (log_b (M) - log_b (N) = log_b (M/N)), and Power Rule (log_b (M^p) = p * log_b (M)) to condense or expand equations .

The Golden Rule: Always verify your solutions! Because you cannot take the log of a negative number or zero, any solution that results in a negative argument must be discarded .
CHAPTERS & TIMESTAMPS
00:00 – Intro & Subscribe
00:34 – What we'll learn today
00:57 – Log to Exponential Form: The Golden Rule
01:46 – One-to-One Properties of Logs
02:46 – Example 1: log_{x^{1/2}} 64 = 3 (3 methods)
06:27 – Example 2: log_3 (x^2) = -8
07:58 – Example 3: log_5 (4t+7) - log_5 t = 2 (Quotient Rule)
10:38 – BONUS: Exponential Functions & Natural Log
11:24 – The constant e ≈ 2.71828
11:50 – What is Natural Log (ln)?
13:16 – Example 4: 17^x = 6 (Using log & ln)
16:59 – Why we use approximations (Irrational numbers explained)
17:50 – Example 5 (Challenge): e^{2x+4} - e^x = 10
21:45 – Your Turn! Solve & comment your answer below
22:30 – Coming soon: Calculus
22:38 – Thanks for watching! 👍

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