Use the properties of logarithms to expand the expression.
log6 36x^5
log6 36x^5 = log6 36 + log6 x^5 = 2 + 5log6 x
To expand the expression log6 (36x^5) using the properties of logarithms, we can use the rule:
log(base a) (b*c) = log(base a) (b) + log(base a) (c)
In this case, we have log6 (36x^5), which can be written as:
log6 (36) + log6 (x^5)
Now let's simplify each logarithm separately:
1. log6 (36):
To determine the value of log6 (36), we need to find the exponent to which we need to raise 6 to get 36.
6^2 = 36
Therefore, log6 (36) = 2.
2. log6 (x^5):
To determine the value of log6 (x^5), we need to find the exponent to which we need to raise 6 to get x^5.
6^(x^5) = x^5
Therefore, log6 (x^5) = x^5.
Now we can substitute these values back into the expanded expression:
log6 (36x^5) = 2 + x^5
Therefore, the expanded expression is 2 + x^5.