Answer:
To prove that logₐ(4) equals 1/log₄ₐ, we used the property of logarithms for the reciprocal and the definition of log₄ₐ to show the required equality.
Step-by-step explanation:
To prove that logₐ(4) = 1/log₄ₐ, we need to use the property of logarithms that the logarithm of the reciprocal is the negative of the logarithm. First, let's express 1/log₄ₐ as a logarithm with base ₐ. By definition, log₄ₐ = 1/logₐ(4), which means that 1/logₐ(4) equals log₄ₐ.
Now, let's use the property of logarithms that states: logₐ(1/x) = -logₐ(x). Taking the reciprocal, we get logₐ(4) = 1/log₄ₐ, as required. Hence, we have proved the given logarithmic identity using the properties of logarithms and reciprocals.