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

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To solve the equation 7^2x - 5*7^x - 24 = 0, substituting y = 7^x simplifies the expression to y^2 - 5y - 24 = 0. This quadratic equation can be solved for y, allowing for the determination of x. The initial confusion about the logarithmic aspect is clarified, as the focus is on solving a polynomial equation rather than a logarithmic one. The transformation of the equation is essential for finding the solution. The approach of using y = 7^x is correct and leads to a straightforward solution process.
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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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Let y = 7^x and see where that leads! :-)
 
?

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

7^{2x} - 5 \times 7^x - 24 = 0

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

y^2 - 5y - 24 = 0

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

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