Solve for b if: -8*e^(5-6b)  + 10 = -16

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

-8*e^(5-6b)  + 10 = -16

First we will subtract 10 from both sides:

==> -8e^(5-6b) = -26

Now we will divide by -8:

==> e^(5-6b) = 26/8

==> e^(5-6b) = 13/4

Now we will apply the natural lorarithm to both sides:

==> ln e^(5-6b) = ln (13/4)

We know that ln e^a = a ln e

==> (5-6b) ln e = ln 13/4

We know that ln e = 1

==> (5-6b) = ln 13/4

Now we will subtract 5 from both sides:

==> -6b = ln (13/4) - 5

Now divide by -6:

==> b= [ln(13/4)  - 5]/-6

 

kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

Posted on

-8*e^(5-6b)  + 10 = -16

--8e^(5-6b) = -16 - 10 = -26

e^(5-6b) = -26/-8 = 13/4

 

Take the natural log of both sides:

ln(e^(5-6b) = ln (  13 / 4) = ln(13) - ln(4)

 

5 - 6b = 1.178655

b =( 1.178655 - 5 ) / -6

b = 0.636890833

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