Solve Logarithm Equation 7^2x - 5*7^x - 24 =0

  • Thread starter vt33
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In summary, the conversation discusses solving a logarithm equation and suggests setting y = 7^x to simplify the equation.
  • #1
vt33
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I need to solve 7^2x - 5*7^x - 24 =0. Am I on the right track by starting with 7^2x - 35^x - 24 = 0?
 
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  • #2
Let [itex]y = 7^x[/itex] and see where that leads! :-)
 
  • #3
?

I sorry, can elaborate. Are you talking about ax+by+c=0. If so, I'm still a little confused.
 
  • #4
You did say "logarithm equation" in the title so I assumed you meant you want to solve this equation:

[tex]7^{2x} - 5 \times 7^x - 24 = 0[/tex]

If so then set [itex]y = 7^x[/itex] and since [itex]7^{2x} = \left(7^x\right)^2[/itex] your equation becomes

[tex]y^2 - 5y - 24 = 0[/tex]

which you can easily solve for y from which you can obtain x.
 

FAQ: Solve Logarithm Equation 7^2x - 5*7^x - 24 =0

What is a logarithm equation?

A logarithm equation is an equation in which the unknown variable appears as an exponent. It is solved by using logarithms, which are the inverse functions of exponential functions.

How do you solve a logarithm equation?

To solve a logarithm equation, you need to use the properties of logarithms to rewrite the equation into a form where you can isolate the variable. Then, you can solve for the variable by taking the logarithm of both sides and simplifying the equation.

What are the properties of logarithms?

The three main properties of logarithms are the product property, the quotient property, and the power property. These properties allow you to manipulate logarithmic expressions and equations in order to solve them.

What does the solution of a logarithm equation represent?

The solution of a logarithm equation represents the value of the variable that makes the equation true. In other words, it is the value that satisfies the equation.

How do you solve the equation 7^2x - 5*7^x - 24 = 0?

To solve this specific logarithm equation, you would first use the power property to rewrite the equation as (7^x)^2 - 5*7^x - 24 = 0. Then, you can substitute the variable a = 7^x to get a quadratic equation (a^2 - 5a - 24 = 0). This can be factored to get the solutions a = 8 or a = -3. Finally, you can substitute back in for a to get the solutions x = log7(8) or x = log7(-3).

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