Question

Find the solution.

Answer 1

\[e ^{-2x}=7\]
\[\ln e ^{-2x}=\ln 7\]
?

Answer 2

Please show step by step?

Answer 3

\[ln[ e^x] = x\]

Answer 4

\[ e^{-2x}=7\]
\[\ln{[e^{-2x}]}=\ln{7}\]
\[-2x =\ln{7}\]
\[x = \frac{\ln{7}}{-2}\]

Answer 5

where did the e go? @freewilly922

Answer 6

The natural log (ln) is the inverse function of the exponential function e.
\[e^{\ln{x}}=x\] and \[\ln{(e^x)} = x\]

Answer 7

so anytime i have a function w/e, if i take the log or natural log, the e cancels?

Answer 8

Yes, thats the whole reason for the natural log. So we can play with the exponents.

Answer 9

Not the log thought. Natural log. Log usually implies log base 10.
\[log_{10} 10^x = x\]

Answer 10

gotcha! thanks :)