QuestionSolve Problems 26-33 for x exactly without using a calculator.
26. $\log (x+5)=\log (2 x-3)$
27. $2 \ln (x-1)=\ln \left(x^{2}-5\right)$
28. $9^{x-1}=3^{1+x}$
29. $e^{2 x}=e^{x^{2}-3}$
30. $2 x^{2} e^{x}=3 x e^{x}$
31. $\log _{1 \beta} 9=x$
32. $\log _{x} 8=-3$
33. $\log _{9} x=\frac{3}{2}$

Studdy Solution
Problem 33: Solve $\log_9 x = \frac{3}{2}$.
Rewrite in exponential form:
$$9^{3/2} = x$$
Calculate $x$:
$$x = (3^2)^{3/2}$$ $$x = 3^3$$ $$x = 27$$
The solutions are:
26. $x = 8$
27. $x = 3$
28. $x = 3$
29. $x = 3$ or $x = -1$
30. $x = 0$ or $x = \frac{3}{2}$
31. $x = \frac{\log 9}{\log (1/\beta)}$
32. $x = \frac{1}{2}$
33. $x = 27$