How to Solve Logarithmic Equations Quickly and Easily?

  • Thread starter omg precal
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    Logarithms
In summary, we reviewed several equations involving logarithms and exponents. We learned that when adding logarithms with the same base, we can multiply the contents inside the log. We also saw that taking the square root of an equation can help solve for the variable. Finally, we used the power rule to simplify an equation and solve for x. Remember to always show your work when seeking help.
  • #1
omg precal
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Homework Statement



3^(x - 2) = 30

(x - 2)^3 = 30

log (base 4) (x + 3) + log (base 4) (x - 3) = 2

the square root of: (4^(x + 3) / 16^x) = 32

log (base 9) x = 1.5

Homework Equations



NONE

The Attempt at a Solution



I haven't done this since last year. Someone refresh my memory. Please show me how to do it and fast fast fast! Thanks in advance.
 
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  • #2
omg precal said:
I haven't done this since last year. Someone refresh my memory. Please show me how to do it and fast fast fast! Thanks in advance.
you need to show work b4 help is given.
 
  • #3
i struggled but finally got every one but this one:

log (base 4) (x + 3) + log (base 4) (x - 3) = 2

just get me started please. thanks.
 
  • #4
i know there is a rule that if they are the same base logs, u can do something to them but idk really!
 
  • #5
the way logs are read ... log(base)y=x

the base must be raised to some power x to get y

show an attempt at all of your questions and i will work them all out!
 
  • #6
ok i think i vaguely remember that if u add logs with the same base, you can multiply what is in the log. that woiuld make it:

log base 4 of x^2 - 9 = 2

meaning 16 = x^2 - 9

meaning x^2 = 25

meaning x = 5

hooray, thanks!
 
  • #7
omg precal said:
ok i think i vaguely remember that if u add logs with the same base, you can multiply what is in the log. that woiuld make it:

log base 4 of x^2 - 9 = 2

meaning 16 = x^2 - 9

meaning x^2 = 25

meaning x = 5

hooray, thanks!
excellent :) the first 2 are ez since now you've solved this one ... the square root one, i'll work

square both sides

4^(x+3)/4^(2x) = 32^2

4^(x+3-2x) = 32^2 (simplify your exponent, take the log of both sides, use one of the rules of the power rule, bring down the exponent)

x = 3 - log(32^2)/log(4)
 
Last edited:
  • #8
done em all, thanks roco
 

1. What is a logarithm?

A logarithm is a mathematical function that calculates the power or exponent needed to produce a given number. In other words, it is the inverse of an exponential function.

2. Why are logarithms important?

Logarithms are important in many fields of science, such as physics, chemistry, and engineering. They are used to simplify complex calculations, convert between different units of measurement, and analyze data.

3. How do I solve logarithmic equations?

To solve a logarithmic equation, you can use the properties of logarithms, such as the product and quotient rules, to simplify the equation. Then, you can use the properties of exponents to isolate the variable.

4. What are some common uses of logarithms?

Some common uses of logarithms include measuring the intensity of earthquakes and sound waves, pH levels in chemistry, and the loudness of music. They are also used in financial calculations, such as compound interest and population growth.

5. What are some common mistakes when working with logarithms?

Some common mistakes when working with logarithms include forgetting to apply the properties of logarithms correctly, mixing up the base of the logarithm, and forgetting to include the absolute value when taking the logarithm of a negative number. It is important to double-check your work and be familiar with the rules of logarithms to avoid these mistakes.

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