Solution assignment 04 Logarithmic equations

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Assignment 4

Solve:

$\ln(x)[\ln(x)-3]=-2$

Solution

The domain is defined by the function $\ln(x)$ and is equal to $x>0$ (of course $\ln(x)\neq3$ , i.e. $x\neq{e^3}$ , or $\ln(x)\neq0$ , i.e. $x\neq1$ ).
We work out the equation:

$\ln^2(x)-3\ln(x)+2=0$

We substitute into the equation:

$y=\ln(x)$

and get:

$y^2-3y+2=0$

This equation can be factorized:

$(y-2)(y-1)=0$

and has the solutions:

$y=1$ or $y=2$

Thus the corresponding solutions for $x$ are:

$\ln(x)=1$ and thus $x=e$

$\ln(x)=2$ and thus $x=e^2$

Both solutions lie in the domain and are valid.

Return to Assignments Logarithmic equations

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Solution assignment 04 Logarithmic equations

Assignment 4

Solution

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