1. ## logarithmic functions

right now, we're learning about logs functions and whatnot. i find it quite hard to understand. i hope that you can help me understand log functions better by showing a step by step procedure of how to solve these problems. hints and tips are much appreciated!<3

solve for x.

thankyouuu!

2. Originally Posted by ninjuhtime
right now, we're learning about logs functions and whatnot. i find it quite hard to understand. i hope that you can help me understand log functions better by showing a step by step procedure of how to solve these problems. hints and tips are much appreciated!<3

solve for x.

thankyouuu!

#1

$e^{x+5}/e^5=e^{x+5-5}=e^x.$

so you have $e^x=3$

Answer: $x=ln3$

#3

$e^{2lnx-ln(x^2+x-3)}=1$ Remember if something to the power something (for example $a^b$) equals 1 the power is 0. (If $a^b=1$ then $b=0$)

So in your case $2lnx-ln(x^2+x-3)=0$ Using the fact that $2lnx=lnx^2$ you get $lnx^2-ln(x^2+x-3)=0$

This means "contents" of the logarithms are the same so $x^2=x^2+x-3$

Answer $x=3$

Try to solve # 2 by yourself.

3. thank you so much for the help! but what about the base e? does it affect the answer? also i learned from my teacher that $e^x$ is supposed to equal something. when e to the power of any constant equals 0, right?

4. Originally Posted by ninjuhtime
thank you so much for the help! but what about the base e? does it affect the answer? also i learned from my teacher that $e^x$ is supposed to equal something. when e to the power of any constant equals 0, right?

Base is included in $Ln$ another words, $Log$ with base $e$ is $Ln$. Remember treat $e$ as a number, it is just $2.73.....$. so of course $e^x$ should equal something and that something depends on $x$. $e^3=e*e*e$, if power is $x$ it will be a product of $e$ $x$ times. No it is not right $e^{any constant}$ is not zero. Only power minus infinity makes it zero. Probably your teacher meant derivative....