If e^6x = 4 then x =?

Question

possible solutions...

a. (1/3) ln 2

b. (1/2) ln 2

c. (2/3) ln 2

d. (5/6) ln 2

e. none of these

Answer 1

put ln on both sides

ln(e^6x) = ln4

6x = ln4

x = (ln4)/6

x=ln(2^2)/6

x=2ln2/6

x=(1/3)ln2

Answer 2

e^(6x) = 4 ==> ln(4) = 6x ==> x = (1/6)*ln(4) = (1/6)*ln(2^2) = (1/3)*ln(2).

So, a).

I used the fact that a^b = c is equivalent to log_a(c) = b, and that ln is log_e. I'm using the underscore as a shorthand for the subscript or base of the log. And don't forget that ln(a^b) = b*ln(a).

Answer 3

I'm guessing you mean that e is raised to the power of 6x.
Right? If so
e^(6x)=4
Ln(e^(6x))=Ln(4)
6x = Ln(4)
x = Ln(4)/6
Ln(4) = Ln(2^2) = 2Ln(2)
So x = 2Ln(2)/6 = 1/3Ln(2)

Pick a.

Answer 4

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