does ln e^10=1 or 10?

Question

zepdrix · Answer

Hey you :) Welcome to OpenStudy!

zepdrix · Answer

$$\Large\rm \log(a^b)=b \log(a)$$

zepdrix · Answer

Therefore,$$\Large\rm \ln(e^{10})=10 \ln(e)$$

zepdrix · Answer

Do you remember what happens when the `base` of the log is the same as the inside? :)

zepdrix · Answer

Examples:
$$\Large\rm \log_2(2)=1$$$$\Large\rm \log(10)=1$$$$\Large\rm \ln(e)=\log_e(e)=?$$

anonymous · Answer

well, I know that ln e=1, but depending on the way you enter the equation into the calculator, I get both answers 1 and 10

zepdrix · Answer

This is how you would want to enter it into the calculator:

$\Large\rm \ln(e\text{^}(10))$
Was entering it a different way giving you 1 somehow? :o

anonymous · Answer

i typed ln (e^10) and got ten, i typed ln (e)^10 and got one, so i wasn't sure which was correct. Thank you :)

anonymous · Answer

your calculator has two logs one base ten and one base e

zepdrix · Answer

Ahh I see what you did ^^
The second way, your calculator is interpreting it as: $\Large\rm (\ln e)\text{^}(10)$
So it did the log BEFORE it did the 10,
$\Large\rm (1)\text{^}(10)=1$
Yah that's no bueno c: try to avoid silly mistakes like that hehe.

anonymous · Answer

we just started this unit today, so i'm a bit new :) i'll try and avoid these mistakes in the future. so to clarify the answer IS 10, correct?

zepdrix · Answer

yes, good c:

anonymous · Answer

thank you! this helps very much :)