Can this equation be solved explicitly for x
$\displaystyle y=2.3^x + 7^x$
That is not the question (but you can see that y cannot be zero or negative starting in two lines...)
$\displaystyle y = a^x + b^x$
$\displaystyle \ln y = x \ln a + x \ln b$
$\displaystyle \ln y = x (\ln a + \ln b)$
$\displaystyle \ln y = x (\ln ab)$
Can you take it from here?