Show that there is exactly one real number

for which

. Find the integer part of this number. State any theorems you use in your solution.

My attempt:

By the intermediate value theorem, the continuous function crosses the x axis. The function is always increasing, therefore it crosses the x axis only once.

Is there an algebraic way for finding the integer part? I just subbed 1 into the original equation and got an answer < 5 then subbed in 2 and got an answer > 5 and deduced that x must be 1.something

the integer part is 1.