How do you solve 1-2e^(2x)=-19?

3 Answers
May 1, 2018

x = ln \sqrt{10}

Explanation:

1 - 2 e^{2x } = -19

-2 e^{2x} = -19 -1 = -20

e^{2x} = -20/(-2) = 10

ln e^{2x} = ln 10

2x = ln 10

x = {ln 10}/2 = ln \sqrt{10}

Check:

1 - 2 e^{2x }

= 1 - 2 e^{2 (ln sqrt{10} ) }

= 1 - 2 e^{ln 10}

= 1 - 2(10)

= -19 quad sqrt

the value is ~~1.151

Explanation:

given 1-2e^(2x)=-19rArr-2e^(2x)=-20rArre^(2x)=10
in general we have e^m=krArr log_ek=m
which means we have log_e10=2x and log_e10~~2.302
we have 2x=2.302rArrx~~1.151

May 1, 2018

x = (ln10)/2
~~1.1512925465

Explanation:

Subtract 1 on both sides.
-2e^(2x) = -20
Divide by -2.
e^(2x) = 10
Taking the logarithm of both sides, we have:
ln(e^(2x)) = ln10
Using the power rule of logarithms,
2xln(e) = ln 10

lne = 1 So, we have:

2x = ln 10
x = (ln10)/2