Question

Natural logs

Answer 1

e^x is the inverse operation of log(x)

if
\[y = lnx\]then\[x = e^y\]
also:\[e^{lnx} = \ln(e^x) = x\]


so with :\[e^{x+2} = 0.5\]take ln of both sides gives:\[\ln(e^{x+2}) = \ln(0.5)\]\[x+2 = \ln(0.5)\]

Answer 2

next one: take ln of both sides:

\[\ln (e^{0.5x}) = \ln(t)\]\[0.5x = \ln(t)\]

Answer 3

Thank you

Answer 4

glad i could help ^_^

btw, first line i replied with should have said: e^x is the inverse of ln(x)

while b^x is inverse of log_b(x)