Logarithms Explained Rules & Properties, Condense, Expand, Graphing & Solving Equations Introduction

Logarithms Defined Guidelines & Properties, Condense, Increase, Graphing & Fixing Equations Introduction

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This algebra 2 / precalculus math video tutorial explains the foundations and properties of logarithms. It reveals you how you can condense and increase a logarithmic expression along with graphing and fixing logarithmic equations.

Algebra For Novices: https://www.youtube.com/watch?v=MHeirBPOI6w
Algebra 2 – Fundamental Introduction: https://www.youtube.com/watch?v=i6sbjtJjJ-A
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Fractions – Fundamental Introduction: https://www.youtube.com/watch?v=GvLIEiqxS6s
How To Clear up Linear Equations: https://www.youtube.com/watch?v=7DPWeBszNSM
Linear Equations – Take a look at Assessment: https://www.youtube.com/watch?v=Ft2_QtXAnh8
How To Issue Trinomials: https://www.youtube.com/watch?v=-4jANGlJRSY
Techniques of Linear Equations – 2 Variables: https://www.youtube.com/watch?v=oKqtgz2eo-Y
Quadratic Equations – Take a look at Assessment: https://www.youtube.com/watch?v=fFFA7Q4eVuY
Multiplying Rational Expressions: https://www.youtube.com/watch?v=RROSgr4oXjU
Graphing Rational Capabilities: https://www.youtube.com/watch?v=bWVhwYdSnfk
Radical Expressions – Take a look at Assessment: https://www.youtube.com/watch?v=wOcc5EoOojE
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Logarithms – The Straightforward Manner! https://www.youtube.com/watch?v=kqVpPSzkTYA
Log to Exponential Type: https://www.youtube.com/watch?v=f0C1KL7GkqY
Change of Base System: https://www.youtube.com/watch?v=FFm-zaFW_X4
Change of Base Log Drawback: https://www.youtube.com/watch?v=p7hD9VdXv9U
Properties of Logarithms: https://www.youtube.com/watch?v=Jtv9Lnf7Zw8
Increasing Logarithmic Expressions: https://www.youtube.com/watch?v=OIz-5MyJA3g
Condensing Logarithmic Expressions: https://www.youtube.com/watch?v=luRrOlsB4cY
Pure Logarithms: https://www.youtube.com/watch?v=daUlTsnCNRQ
Fixing Exponential Equations: https://www.youtube.com/watch?v=9tutJ5xrRwg
Exponential Equations – Quadratic System: https://www.youtube.com/watch?v=1_XHAzgUi1o
Exponential Equations – Quadratic Type: https://www.youtube.com/watch?v=yNgmVu0R_T8
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Fixing Logarithmic Equations: https://www.youtube.com/watch?v=fnhFneOz6n8
Logarithmic Equations – More durable Examples: https://www.youtube.com/watch?v=PIx0Z0LqqFY
Logarithmic Equations – Completely different Bases: https://www.youtube.com/watch?v=XvwPB21Gm9A
Exponential Logarithmic Equations: https://www.youtube.com/watch?v=6CrXFvvwsaE
Graphing Logarithmic Capabilities: https://www.youtube.com/watch?v=-nptxS9rZNA
Graphing Exponential Capabilities: https://www.youtube.com/watch?v=DASfP8KAyvs
Graphing Pure Log Capabilities: https://www.youtube.com/watch?v=ymXD6xCmzJE
Compound Curiosity Phrase Issues: https://www.youtube.com/watch?v=Hn0eLcOSQGw
Curiosity Compounded Repeatedly: https://www.youtube.com/watch?v=Ln97Hd7AiDc
Inhabitants Development Phrase Issues: https://www.youtube.com/watch?v=k4LLdFFLRmQ
Logarithms Apply Issues: https://www.youtube.com/watch?v=7DVbQKI600ok
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The place does “e” come from? https://www.youtube.com/watch?v=pDFcu_wLOzo
Advanced Logarithmic Equations: https://www.youtube.com/watch?v=k7m2z0bX_tg
Exponential Equations – Powers of X: https://www.youtube.com/watch?v=ec_9rkWxrYA
Exponential Equations With Radicals: https://www.youtube.com/watch?v=d-E5isaIDTA
Tough Exponential Equations: https://www.youtube.com/watch?v=F1b1beR3sNk
Inverse of Logarithmic Capabilities: https://www.youtube.com/watch?v=hNsvGz7JPJQ
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Capabilities – Take a look at Assessment: https://www.youtube.com/watch?v=1xATmTI-YY8
Algebra 1 Assessment Research Information: https://www.youtube.com/watch?v=TbJ5gqLRpeM
Algebra Closing Examination Assessment: https://www.youtube.com/watch?v=U0Y8nSmEpNM
Precalculus Closing Examination Assessment: https://www.youtube.com/watch?v=Tj-V6KnwM5w
Full Size Examination Movies + Worksheets: https://bit.ly/4990rzU

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45 thoughts on “Logarithms Defined Guidelines & Properties, Condense, Increase, Graphing & Fixing Equations Introduction”

  11. Love this tutor, BUT…. at the 48 min, the problem 8^x+4 = 16^2x, the solution is not 24/5 but 12/5. I know this because when I plugged in 12/5 or 2.4 for x in both sides of the equation, I get an identity 602,248.7631. When I used the Organic Chemistry Tutor's answer, the left side of the equation yields a value of 88,550,676.93, and the right side equals 154,175,683.4, or about 1.75 times bigger.

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  22. ๐ŸŽฏ Key Takeaways for quick navigation:

    00:27 ๐Ÿง  When evaluating logarithms, ask yourself what power the base must be raised to get the given number.
    02:21 ๐Ÿ“ Logarithms can be evaluated by counting the number of times a base must be multiplied to reach a given number.
    04:03 ๐Ÿ”ข The logarithm of 10 is 1, log of 100 is 2, log of 1000 is 3, and so on. Counting zeros in the number gives the logarithm base 10.
    05:49 โš ๏ธ Logarithm of 0 and logarithm of a negative number are undefined.
    08:32 ๐Ÿ“ The change of base formula: log base a of b can be expressed as log base c of b divided by log base c of a.
    12:45 ๐Ÿ“ˆ Properties: log(a) + log(b) = log(a * b), log(a) – log(b) = log(a / b), log(a^2) = 2 * log(a).
    14:23 โž— When condensing log expressions with addition or subtraction, positive terms go on top, negative terms on the bottom.
    16:36 ๐Ÿ”„ When condensing log expressions with coefficients, use the power rule and move the coefficients to the exponents.
    20:36 ๐ŸŒ Expanding log expressions involves distributing the exponents and simplifying the result.
    22:22 ๐Ÿ”„ Simplifying expressions involving natural logarithms often involves canceling out the ln and e terms.
    24:50 ๐Ÿงฉ When solving logarithmic equations, converting to exponential form helps find the unknown variable.
    28:05 ๐Ÿ”„ Exponential form to logarithmic form conversion involves setting the exponent as the log result.
    30:48 โžก๏ธ Solving logarithmic equations involves converting them to exponential form and solving for the variable.
    31:57 ๐Ÿงฎ When solving equations with logarithms, apply inverse operations, such as subtraction or division, to isolate the variable.
    33:28 ๐Ÿ“Š When dealing with multiple logarithms, condense them into a single logarithm using multiplication to simplify problem-solving.
    36:54 ๐Ÿšซ Be cautious of extraneous solutions when solving logarithmic equations, as they might lead to invalid results.
    37:26 ๐Ÿ“ When combining logarithmic expressions, use addition for expressions with different bases, and multiply for expressions with the same base.
    48:11 ๐Ÿง  When faced with an exponential equation with different bases, try to express them in a common base for easier comparison and solution.
    54:28 ๐Ÿ“ˆ Determine the domain of a logarithmic function by ensuring that the argument inside the logarithm is greater than zero.
    01:00:13 โ†”๏ธ To find the inverse function of a logarithmic function, switch x and y, solve for y, and replace y with the inverse function symbol.
    01:01:46 ๐Ÿ“Š Graphs of exponential functions and logarithmic functions are inversely related, demonstrating the fundamental connection between them.
    01:02:42 ๐Ÿ“ˆ Exponential functions have horizontal asymptotes, and the equation for the horizontal asymptote can be found using the external number in the exponential function. For example, if it's 2^x + 1, the horizontal asymptote is y = 1.
    01:03:11 ๐Ÿ“‰ Logarithmic functions have vertical asymptotes, and the equation for the vertical asymptote can be found by setting the inside of the logarithm equal to 0. For example, log base 2 (x – 3) implies a vertical asymptote at x = 3.
    01:03:24 ๐Ÿ“Š Once you have asymptotes and two points, you can graph an exponential function. Start by plotting the asymptotes and then follow the points to graph the curve.
    01:05:42 ๐Ÿ”„ The horizontal asymptote for an exponential function is the number outside the exponential part. For example, in the function e^(x – 1) – 2, the horizontal asymptote is y = -2.
    01:08:05 ๐Ÿ“‰ For functions like 2^(4 – x), find the points by setting the exponent equal to 0 and 1. Plug these values into the equation to get points for graphing. The horizontal asymptote is the number outside the exponential part.
    01:11:21 ๐Ÿ“Š To graph logarithmic functions like log base 2 (x – 3), find the vertical asymptote by setting the inside part equal to 0. Then, find additional points by setting the inside equal to 1 and the base (2 in this case).
    01:13:22 ๐ŸŒ The domain of a logarithmic function is determined by the vertical asymptote and the highest x value. The range is always from negative infinity to infinity.
    01:14:33 ๐ŸŒ Exponential function domains are all real numbers, but their ranges are limited. For example, a horizontal asymptote at y = 1 limits the range to 1 to infinity.
    01:15:42 ๐Ÿ”„ For logarithmic functions like ln(x – 1) + 2, find the vertical asymptote by setting the inside equal to 0. Then, find additional points for graphing. The range is from negative infinity to infinity.
    01:18:51 ๐Ÿ“ˆ When graphing log base 3 (2 – x) + 1, find the asymptotes by setting the inside of the logarithm equal to 0, 1, and the base (3 in this case). The graph reflects over the y-axis due to the negative sign in front of x.

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