Question 324410
How do you simplify log base5 4 + log base5 250?

log5 (4) + log5 (250)
these both have the same base which is 5
logarithmic rule: logb (m) + logb (n) = logb (mn)
log5 (4) + log5 (250) = log5 (4 * 250) = log5 (1000)
converting to base 10
logarithmic rule: logb (x) = logk (x) / logk (b) where b is old base, and k is the new base
log5 (1000) = log10 (1000) / log10 (5) = 3 / log10 (5)
log10 (5) = approximately 0.698970 rounded to 6 decimal places
log5 (1000) = approx. 4.292030 rounded to 6 decimal places