Question

onsider the equation 0.5 times e4z =13 solve the equation for z. express the solution as a logarithm in base e

Answer 1

Answer:

$z=\frac{ln(26)}{4}$

Step-by-step explanation:

The given equation is:

$0.5\,e^{4z}=13$

so, we first isolate the exponential form that contains the unknown "z" in the exponent, by dividing both sides by 0.5:

$0.5\,e^{4z}=13\\e^{4z}=\frac{13}{0.5}\\e^{4z}=26$

Now we bring the exponent down by applying the natural log function on both sides, and then solve for "z":

$e^{4z}=26\\ln(e^{4z})=ln(26)\\4\,z=ln(26)\\z=\frac{ln(26)}{4}$