Logarithm Properties: Proving y = b^c sqrt(x) from log equation

Learn how to use logarithm properties, including the power and product rules, to transform logarithmic equations and solve for y, demonstrating y = b^c sqrt(x).

Answer

Based on the image provided, the problem is as follows:

Problem:
Show that if

, then

Step-by-step Solution:

Start with the given equation:
Use the power property of logarithms, which states that . Apply this to the term :
Recall that is equivalent to :
Express the constant as a logarithm with base . Since , we can substitute:
Use the product property of logarithms, which states that :
Remove the logarithms from both sides (by taking the base exponential of both sides):

Conclusion:
We have shown that if

, then

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Logarithm Properties: Proving y = b^c sqrt(x) from log equation

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