Assignments

In the assignments below logarithmic equations must be solved. Note that a logarithm is defined for an argument greater than $0$ . When the equation contains more than one logarithm all of these conditions have to be met (they define the so-called domain of the equation). When a solution is found it is valid if it lies in the domain.

1. Solve:

$\ln(x+4)=2$

2. Solvep:

$\displaystyle\frac{\ln(x+1)}{4}=-1$

3. Solve:

$\log(\displaystyle\frac{x+1}{x})=1$

4. Solve:

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

5. Solve:

$3\ln(x)+2\ln(x^2)=6$

6. Solve:

$\ln(2x+1)+\ln(x+2)=\ln(x+10)$

7. Solve:

$\ln(2-x)=1+\ln(x)$

8. Solve:

$\ln[(x+8)(x-2)]=\ln(75)$

9. Solve:

$\log_2(x)+\log_2(x-2)=3$

10. Solve:

$\ln(x+2)+\ln(x-3)=\ln(x-1)+\ln(x+4)$

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