Use the definition of logarithm to simplify each expression.
text((a) )log_(3b) \(3b\)
text((b) )log_(4b) \((4b)^6\)
text((c) )log_(7b) \((7b)^(-11)\)
To simplify each expression using the definition of a logarithm, we can write the logarithm equation in exponential form.
(a) For \( \log_{3b}3b \):
We can rewrite this equation as \( 3b = (3b)^1 \), since any number raised to the power of 1 is equal to itself.
Therefore, the simplified expression is \( \boxed{(a) \, 3b} \).
(b) For \( \log_{4b}(4b)^6 \):
By applying the definition of a logarithm, we can rewrite this equation as \( (4b)^6 = (4b)^{\log_{4b}(4b)^6} \).
Since the base of the logarithm and the base of the exponentiation are the same, we can simplify this to \( (4b)^6 = (4b)^6 \).
Therefore, the simplified expression is \( \boxed{(b) \, (4b)^6} \).
(c) For \( \log_{7b}(7b)^{-11} \):
By using the definition of a logarithm, we can rewrite this equation as \( (7b)^{-11} = (7b)^{\log_{7b}(7b)^{-11}} \).
Since the base of the logarithm and the base of the exponentiation are the same, we can simplify this to \( (7b)^{-11} = (7b)^{-11} \).
Therefore, the simplified expression is \( \boxed{(c) \, (7b)^{-11}} \).