Answer:
Option C
Step-by-step explanation:
Given expression in the question is,
y = [tex]7(2)^{\frac{t}{30}}[/tex]
To get the value of t,
[tex]\frac{y}{7}=2^{\frac{t}{30}}[/tex]
Take the log on both the sides of the expression,
log([tex]\frac{y}{7}[/tex]) = [tex]\text{log}[(2^{\frac{t}{30}})][/tex]
log([tex]\frac{y}{7}[/tex]) = [tex]\frac{t}{30}(\text{log2})[/tex]
t = [tex]30(\frac{\text{log}\frac{y}{7}}{\text{log}2} )[/tex]
t = [tex]30[\text{log}_2(\frac{y}{7})][/tex] [Since, [tex]\frac{\text{loga}}{\text{logb}}=\text{log}_a(b)}[/tex]]
Therefore, Option C will be the answer.
