log5(15)+log5(405)−5log5(3) =?
regardless of the base,
log15+log405-5log3
= log(15*405/3^5) = log(25)
Since we are using base 5,
log_5(25) = 2
since 5^2 = 25
thank you
To compute the value of the expression log5(15) + log5(405) - 5log5(3), we will use the properties of logarithms.
1. First, let's simplify each term individually using the logarithmic identities:
log5(15) = log5(3 * 5) = log5(3) + log5(5) = log5(3) + 1
log5(405) = log5(3 * 3 * 3 * 3 * 5) = log5(3^4 * 5) = 4 * log5(3) + 1
5log5(3) = log5(3^5) = 5 * log5(3)
2. Now, substitute the simplified expressions back into the original expression:
log5(15) + log5(405) - 5log5(3) = (log5(3) + 1) + (4 * log5(3) + 1) - (5 * log5(3))
3. Combine like terms:
= log5(3) + 1 + 4 * log5(3) + 1 - 5 * log5(3)
= 6 * log5(3) + 2 - 5 * log5(3)
= (6 - 5) * log5(3) + 2
= log5(3) + 2
Therefore, log5(15) + log5(405) - 5log5(3) simplifies to log5(3) + 2.