quick question

[renegade05]

I am getting conflicting information...

Please help me clarify:

\(\displaystyle \frac{d}{dx}5^x=5^xln(5)\)
\(\displaystyle \frac{d}{dx}5^x=5^xlog(5)\)

which one is correct?

Thanks!

 

[tkhunny]

Both!!!!

In pre-calculus mathematics, "log" is often used to mean Base 10 logs. When one gets to calculus, this becomes tiresome as the "Natural Logarithm" is so often encountered. Therefore, 'log" tends to mean Base e, not base 10. If a distinction is necessary, feel free to emphasize it.

\(\displaystyle log_{10}(x)\) is okay.

\(\displaystyle log_{e}(x)\) is okay.

\(\displaystyle ln_{10}(x)\) is not okay.

\(\displaystyle log(x)\) is okay, but may need clarification. If the context is clear, just leave it.

Just make the transition. That's all.

Of course, your calculator maintains log for base 10 and ln for base e.