Example 4. Solve the equation

$$
\sqrt{3^{x}} 5^{x / 2}=225
$$

The solution. Since $\sqrt{3^{x}} 5^{x / 2}=3^{x / 2} 5^{x / 2}=15^{x / 2}$, the original equation is equivalent to the equation $15^{x / 2}=15^{2}$, i.e., $x=4$.

An equation of the form

$$
a^{f(x)}=1, \quad a>0, \quad a \neq 1
$$

is equivalent to the equation $f(x)=0$.

Example 5. Solve the equation

$$
10^{x^{2}+x-2}=1
$$
Solution. The given equation is equivalent to the equation $x^{2}+$ $+x-2=0$. Therefore, the given equation has two roots: $x_{1}=-2, x_{2}=1$.