Answer:
[tex]z=\frac{ln(26)}{4}[/tex]
Step-by-step explanation:
The given equation is:
[tex]0.5\,e^{4z}=13[/tex]
so, we first isolate the exponential form that contains the unknown "z" in the exponent, by dividing both sides by 0.5:
[tex]0.5\,e^{4z}=13\\e^{4z}=\frac{13}{0.5}\\e^{4z}=26[/tex]
Now we bring the exponent down by applying the natural log function on both sides, and then solve for "z":
[tex]e^{4z}=26\\ln(e^{4z})=ln(26)\\4\,z=ln(26)\\z=\frac{ln(26)}{4}[/tex]
