Solving Log Equations: How to Use Logarithmic Properties | Homework Help

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In summary, the conversation discusses solving the equation log base 7 (7x+8) = log base 7 (7x+3) and concludes that there is no solution to this equation. This is because the expressions on both sides of the equation use the same base for the logarithm and the arguments of the log functions are not equal.
  • #1
KatieLynn
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Homework Statement


Solve the equation
log base 7 (7x+8) = log base 7 (7x+3)

Homework Equations



I don't think you use equations for this, just the properties of logarithms

The Attempt at a Solution



I thought since they have the same base you could set the parts in parenthesis equal to each other

(7x+8) = (7x+3)

so you get
8=3 or
5=0

but that can't be right...
 
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  • #2
Well that should be correct...but if you knew what the graphs looked like, you would see that they are just horizontal shifts of each other...so it is kind of like they are "parallel' or so to say...meaning that they do not intersect
 
  • #3
so that means there is no answer?
 
  • #4
yep...
 
  • #5
KatieLynn said:
so that means there is no answer?

You correctly remarked that if the expressions on both sides of the equation use the same base for the logarithm, then the arguments of the log functions on each side must be equal. So, if you typed this correctly, that would be asking for the value of x such that 7x + 8 = 7x + 3 . You also observed that there is no such value possible. So that is your answer: there is no solution to this equation. (That can happen occasionally in a homework or exam problem, or in Real Life. Demonstrating that a solution doesn't exist can be just as meaningful as finding a solution...)
 

FAQ: Solving Log Equations: How to Use Logarithmic Properties | Homework Help

What is a logarithm and how does it relate to log equations?

A logarithm is the inverse of an exponential function. It is used to solve for the unknown exponent in an exponential equation. In log equations, logarithmic properties are used to simplify the equation and solve for the unknown variable.

What are the basic properties of logarithms?

The basic properties of logarithms are:

  • Product Property: logb(xy) = logb(x) + logb(y)
  • Quotient Property: logb(x/y) = logb(x) - logb(y)
  • Power Property: logb(xn) = n*logb(x)

How do I solve a log equation using logarithmic properties?

To solve a log equation, you need to apply logarithmic properties to simplify the equation. First, use the Product or Quotient Property to combine all the terms with logarithms into a single logarithm. Then, use the Power Property to bring down any exponents. Finally, use the definition of logarithms to solve for the unknown variable.

What are some common mistakes to avoid when solving log equations?

Some common mistakes to avoid when solving log equations include:

  • Forgetting to apply logarithmic properties to simplify the equation
  • Forgetting to check for extraneous solutions
  • Using the wrong base for logarithms
  • Not bringing down exponents correctly using the Power Property

Can log equations be solved without using logarithmic properties?

In some cases, log equations can be solved without using logarithmic properties. This is usually when the equation has a simple form such as logb(x) = c, where c is a constant. In such cases, you can simply rewrite the equation in exponential form and solve for the unknown variable. However, in most cases, logarithmic properties are necessary to solve log equations.

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