Question

solve for x : 1000=500 e^2x

a. x=ln(2)-2
b. x=ln(1000)/2*ln(500)
c. x=ln(2)/2
d. x=1/e

Answer 1

$$\bf 1000=500 e^2x\\
\frac{1000}{500}= e^{2x} \implies 2 = e^{2x}\\
\text{using log cancellation rule of }\\
log_aa^x = x\\
\text{keep in mind that }ln \implies log_e\\
log_e(2) = log_e(e^{2x})\\
log_e(2) = 2x
$$

Answer 2

or
2x = ln(2)

Answer 3

so the answer would be C?