Question

okay can some1 please explain this to me:

i had to solve for x. 6^5x=3000. i came up with the solution x= log 3000/5log6. in my textbook, the answer is x= ln 3000/5ln 6. i put both into my calculator but both are exactly the same thing. my lecturer marked me wrong because i wrote log instead of ln even though both solutions are exactly the same. please tell me whats the difference and how to get to the ln solution instead of the log solution.

Answer 1

Is it:
\[\large 6^{5x} = 3000\]?

Answer 2

yes exactly.

Answer 3

Take log both sides.
\(5xln6 \ = ln3000\)

Answer 4

\[\ln 6^5x=\ln 3000; 5x*\ln6=\ln3000; x=\ln3000/5*\ln6\]

Answer 5

=> \(5xln(6) = ln3000\) => \[5x = \frac{\ln(3000)}{\ln(6)} => x= \frac{\ln(3000)}{\ln(6)} *\frac{1}{5} \]

Answer 6

@Vladislav ... why did you use ln instead of log? because i thought that log rules state that to turn an exponential equation into another form , you use log and i thought you only use ln when you want to change the natural exponential e into log form. for example i would only have used ln if theoretically the equation was this: \[e ^{5x}=3000\]

only if the natural base e was involved would i use ln. so why ln instead of log?

Answer 7

You can use \(ln\) or \(log\) its the same thing. try it on calculator you will see.

Answer 8

if so, x=ln3000/5

Answer 9

no your answer was correct @Vladislav but i just wana know why ln was used instead of log coz they are both exactly the same when typed into a calc

Answer 10

ln e=1; ln e^5x=5x

Answer 11

@Mimi_x3 yeah i did that on my calc and i could see they were the same thing but i got marked wrong for writting log instead of ln

Answer 12

You can use ln for any reason, it is very useful in engineering calculations)

Answer 13

so just to clarify i shouldnt have been markd wrong because the are exactly the same?

Answer 14

I guess so..they are the same anway..not sure though.

Answer 15

But I tend to use \(ln\) and I never get marked down.

Answer 16

sweet thanks :)

Answer 17

np