Question

Find the domain of the function $f(x)=\log_2(\log_3 x + \log_4 x)$.

Answer 1

`f(x)=\log_2(\log_3 x + \log_4 x)\\\\D:\log_3x+\log_4x > 0 \wedge x > 0\\\\\log_3x+\log_4x > 0\\(\log x)/(\log 3)+(\log x)/(\log4) > 0\\\log x\left((1)/(\log 3)+(1)/(\log4)\right) > 0\\\log x > 0\\x > 1`

Therefore

`D:x > 1 \wedge x > 0\\D:x > 1`