Question

log2=a and log3=b. what is x in 3^(2^x)=2^(3^x)

Answer 1

take log of both side
\[\Large 3^{(2^x)} = 2^{(3^x)} \\\Large \ln3^{(2^x)} = \ln 2^{(3^x)} \\\Large 2^x\ln3 = 3^x\ln 2\]
Now divide both sides by \(3^x\ln3\) to get \(\large\dfrac{2^x}{3^x} =\left(\dfrac{2}{3}\right)^x = \dfrac{\ln2}{\ln3}\)

Now take log again, you should be able to solve for x from here