[SOLVED] Find the domain and range

**NeedHelp18** · February 18th 2009, 05:06 PM

What is the domain and range of this function?
ln(e^(2x-1))

i dont know if my answer is right but i got x is not 1/2
and y = real numbers??

does this graph look like a normal log one?

i plug in numbers and i keep getting a diagonal line?

**Reckoner** · February 18th 2009, 05:12 PM

Originally Posted by NeedHelp18

What is the domain and range of this function?
ln(e^(2x-1))

i dont know if my answer is right but i got x is not 1/2
and y = real numbers??

When $x=\frac12,$ you have $\ln\left(e^{2x-1}\right)=\ln e^0=\ln1=0\text.$ Why are you excluding that from the domain?

does this graph look like a normal log one?

i plug in numbers and i keep getting a diagonal line?

What is $\ln e^n?$ Or in general, $\log_aa^n?$ Hint: the natural logarithm and the natural exponential function are inverses of each other.

**NeedHelp18** · February 18th 2009, 05:23 PM

i am lost now

so what would be the domain?

all real numbers?

and is my range correct?

**Reckoner** · February 18th 2009, 07:23 PM

Originally Posted by NeedHelp18

i am lost now

so what would be the domain?

all real numbers?

Yes. $e^x$ is defined for all real $x,$ its range is $(0,\infty),$ and $\ln x$ is defined for those values.

and is my range correct?

Yes. The range of $e^x$ covers the entire domain of the natural logarithmic function and the range of the natural logarithmic function is $(-\infty,\infty)\text.$

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