I see. Does that mean that I should not use "log pi" in this case, I should be using "Ln pi"? You must be right because "Ln pi" comes up with right answer.
Your error goes all the way back to the beginning.
\(\displaystyle x = y \implies log_z(x) = log_z(y).\)
Remember about changing BOTH sides of the equation equally. When you take logs of both sides of the equation, you must take logs using equal bases.
What you did was
\(\displaystyle e^x = \pi \implies log_e(e^x) = log_{10}( \pi ) \implies xlog_e(e) \approx 0.497 \implies x * 1 \approx 0.497 \implies x \approx 0.497.\)
That is
WRONG because you took logarithms to different bases. The simple correct way is
\(\displaystyle e^x = \pi \implies log_e(e^x) = log_e( \pi ) \implies xlog_e(e) \approx 1.145\implies x * 1 \approx 1.145 \implies x \approx 1.145.\)
Another correct but somewhat more cumbersome way is
\(\displaystyle e^x = \pi \implies log_{10}(e^x) = log_{10}( \pi ) \implies xlog_{10}(e) \approx 0.497 \implies x * 0.434 \approx 0.497 \implies x \approx \dfrac{0.497}{0.434} \approx 1.145 .\)
It makes no difference what base you choose, but you must be consistent.