Solve Log3x: Steps & Graph Changes for y=log4x

  • Thread starter Buddah
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In summary, a logarithm is a mathematical function that is the inverse of an exponential function. To solve log3x, you need to use the properties of logarithms, specifically the power rule. The steps to solve log3x are to rewrite the equation, raise both sides to the base 3, and simplify and solve for x. When x is multiplied by 4, the graph of y=log3x shifts to the right by 1 unit, and the domain is all positive real numbers while the range is all real numbers.
  • #1
Buddah
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Confused

1.Describe the changes to the graph of y = log4x when x is replaced by 16x2
2.Describe the steps you would say over the phone to explain how to solve the equation log3x +log3(x+2)=1

thanks in advance
 
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  • #2


Is that Log(4x) or Log(base 4) of x? Do you mean 32 by 16x2 or 32x?

Can you please clarify your numbers.
 
  • #3


log(base 4) and its 16x^2
 
  • #4


Well, how does log(base 4)(x) compare to log(base 4)(16*x^2)? Use the rules of logs. Like log(a*b)=log(a)+log(b).
 

1. What is a logarithm?

A logarithm is a mathematical function that is the inverse of an exponential function. It helps in solving equations where the variable is in the exponent.

2. How do you solve log3x?

To solve log3x, you need to use the properties of logarithms, specifically the power rule. First, rewrite the equation as log3(x) = y. Then, raise both sides to the 3rd power to eliminate the logarithm. This will give you x = 3y as the solution.

3. What are the steps to solve log3x?

The steps to solve log3x are:

  1. Rewrite the equation as log3(x) = y
  2. Raise both sides to the base 3
  3. Simplify and solve for x

4. How does the graph of y=log3x change when x is multiplied by 4?

When x is multiplied by 4, the graph of y=log3x shifts to the right by 1 unit. This means that the x-coordinate of each point on the graph is multiplied by 4, while the y-coordinate remains the same.

5. What is the domain and range of y=log3x?

The domain of y=log3x is all positive real numbers, since logarithms are not defined for negative numbers or zero. The range is all real numbers, since the output of a logarithmic function can be any real number.

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