Solve the equation.
e^5x = 2
a. 2/5 e
b. in2/5
c. 5 in 2
d. in5/2
typo those answers contain L's not I's
Using the relation
ln(ex = x
For
e5x = 2
Take natural log on both sides,
ln(e5x) = ln(2)
5x = ln(2)
x = ln(2) / 5
Now make your pick for the answer.
take the ln of both sides
5x=ln2
x= 1/5 ln2
so, none of the choices are correct, unless on answer b you meant 1/5 ln2
To solve the equation e^5x = 2, we need to isolate the variable x. To do this, we can take the natural logarithm (ln) of both sides of the equation. The natural logarithm is the inverse function of the exponential function e^x.
Taking the natural logarithm of both sides, we have:
ln(e^5x) = ln(2)
Since ln(e^x) = x for any positive real number x, the left side simplifies to:
5x = ln(2)
Now, we can solve for x by dividing both sides of the equation by 5:
x = ln(2)/5
The answer is the expression ln(2)/5, so the correct option is:
b. ln(2)/5