log(500) + (7/10)^n * log(2) = 0
Substituting the given logarithmic values:
log(500) + (7/10)^n * 0.301 = 0
Rearranging the equation:
(7/10)^n * 0.301 = -log(500)
Dividing both sides by 0.301:
(7/10)^n = -log(500) / 0.301
Taking the logarithm base 10 of both sides:
log((7/10)^n) = log(-log(500) / 0.301)
Using the logarithmic properties, we can simplify: