Question

ln(x) -ln(4) =6
Please show work

Answer 1

See:
f(x)=lnx^4+e^(4x^2+5)
f '(x)=(x^4)'/x^4+e^(4x^2+5).(4x^2+5)'
f '(x)=(4x^3)/x^4+e^(4x^2+5).(8x)
f '(x)=4/x + 8x.e^(4x^2+5)

Answer 2

ln(x) = 6 +ln(4)

make both sides be raised from e

e^(ln(x)) = e^(6+ln(4))

x = e^(6+ln(4))

property of exponents:

x = (e^6)(e^ln(4))
x = (e^6)(4)
x = 4e^6

Answer 3

i plugged 4e^6 back into the equation, it works

Answer 4

\[\ln x=\ln 4+6\]\[x=e^{\ln 4+6}\]\[x=e ^{\ln4}e^6\]\[x=4e^6\]

Answer 5

\[\ln(\frac{x}{4})=6\]
\[\frac{x}{4}=e^6\]
\[x=4e^6\]