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In the output of your initial question, the unknown x2 has not been isolated, since it appears in both sides. You can formulate step2 in a more friendly way:

step2 = solve((p1/p2).subs(step1)==p1/p2, x1)

Likewise, borrowing an idea from this solution of another question, you can rewrite step3:

step3 = solve((U/R).subs(step2).log().log_expand()==0, x2)
step3

The output is

[x2 == e^(-a*log(a)/(a + b) + a*log(b)/(a + b) + a*log(p1)/(a + b) - a*log(p2)/(a + b) + log(R)/(a + b))]

Let see x2 in a more mathematical notation:

show(x2.subs(step3).canonicalize_radical())

This yields $$ \frac{R^{\left(\frac{1}{a + b}\right)} b^{\frac{a}{a + b}} p_{1}^{\frac{a}{a + b}}}{a^{\frac{a}{a + b}} p_{2}^{\frac{a}{a + b}}} $$