Question

solve without using calculator
5ln(x-2)-2=28
help please, thank you

Answer 1

Treat this like a normal algebra problem. Try to get x by itself by UNDOING the things on the left side one by one.
How do I get rid of the -2 outside of the parenthesis part? By doing the opposite to both sides. +2
How do I get rid of the *5 part? By doing the opposite to both sides.
Next, I have to get rid of the ln, but how do I undo that? Well, I should do the opposite. It turns out the opposite of ln(x) is e^x, where e is the mathematical constant.

Answer 2

\(5 \ln (x-2)-2 = 28 \implies \ln (x-2)^5 = 30\) \[\implies (x-2)^5 = e^{30}\]

Answer 3

i have to solve for x. I got that, e^6 = x-2
but from there how would i solve for x without using the calculator? that is what I get stuck actually

Answer 4

i got e^30 = (e^6)^5
both side has 5 so I can get rid of it

Answer 5

\[(x-2)^5 = e^{30} \implies x = e^6 +2 \]

Answer 6

Perfect so far =) Now just add 2 to both sides.
Leave your answer as x = e^6 + 2

Answer 7

thanks, I dont need to solve for numbers
that's why :D

Answer 8

My pleasure =D

Answer 9

There's not a good way to do e^6 + 2 without a calculator, so they just want you to leave it written that way, the same way math teachers often want your answer to have pi in it still.
Here's the answer from a calculator, if you're interested
http://www.wolframalpha.com/input/?i=e%5E6+%2B+2