6.6.63 ln(7-x)+ln(1-x)=ln(25-x)

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  • Thread starter karush
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In summary, the numbers in the equation 6.6.63 ln(7-x)+ln(1-x)=ln(25-x) represent coefficients and variables in a logarithmic expression used to solve for the value of x. To solve for x, logarithmic terms can be combined and the equation can be exponentiated and solved using algebraic techniques. This equation can be solved analytically, but numerical methods may be necessary if the solution is not a rational number. The values of x must be positive in order for the equation to be valid, with a restriction of x not being greater than 7 or less than 1. This equation has practical applications in fields such as finance, physics, and engineering for solving problems involving exponential
  • #1
karush
Gold Member
MHB
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$\tiny\textbf{6.6.63 Kiliani HS}$
Solve for x give exact form
$\ln{(7-x)}+\ln{(1-x)}=\ln{(25-x)}$

$\begin{array}{rrll}
\textsf{log rules} &(7-x)(1-x) &=25-x \\
\textsf{expand} &7-8x+x^2 &=25-x \\
\textsf{set to zero} &x^2-7x-18 &=0 \\
\textsf{factor} &(x-9)(x+2) &=0 \\
\textsf{zero's} &x&=9, \quad -2 \\
x\le -1\quad\therefore &x&=-2
\end{array}$

I hope...
typo's ?
have to very careful:rolleyes:
 
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  • #2
there will be $x \lt 1$ not -1 so $x=-2$ will be the answer
 

1. What is the significance of the numbers and variables in the equation "6.6.63 ln(7-x)+ln(1-x)=ln(25-x)"?

The numbers and variables in this equation represent the coefficients and variables in a logarithmic function. The numbers 6.6.63 and 25 represent the bases of the logarithms, while x represents the variable in the function.

2. How do you solve the equation "6.6.63 ln(7-x)+ln(1-x)=ln(25-x)"?

To solve this equation, you can use the properties of logarithms to combine the two logarithms on the left side of the equation into one. Then, you can use the inverse property of logarithms to isolate the variable x on one side of the equation. Finally, you can use algebraic methods to solve for the value of x.

3. What is the domain of the function represented by the equation "6.6.63 ln(7-x)+ln(1-x)=ln(25-x)"?

The domain of this function is the set of all real numbers that can be substituted for x without causing any undefined or imaginary results. In this case, the domain would be all real numbers except for 7, 1, and 25, as these values would result in undefined or imaginary results.

4. What is the relationship between the values of x and the solutions to the equation "6.6.63 ln(7-x)+ln(1-x)=ln(25-x)"?

The values of x represent the inputs or independent variables in the equation, while the solutions represent the outputs or dependent variables. In other words, the values of x determine the solutions to the equation.

5. How can this equation be applied in real-world situations?

This equation can be applied in various real-world situations that involve exponential or logarithmic relationships, such as population growth, radioactive decay, and pH calculations. It can also be used in financial calculations involving compound interest or continuously compounded interest.

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