We need to solve the following equation:
[tex]e^{0.006x}=26[/tex]
First, set both sides ln:
[tex]\ln e^{0.006x}=26[/tex]
We can down the exponents and simplify lne=1 :
[tex]0.006x=\ln26[/tex]
Now, divide both sides by 0.006:
[tex]\frac{0.006x}{0.006}=\frac{\ln26}{0.006}[/tex]
Simplify:
[tex]x=\frac{\ln(26)}{0.006}[/tex][tex]x=543.02[/tex]
Hence, the answer is x=543.02 (The answer is rounded to the nearest thousandth)
