Final answer:
The logarithmic form of the equation (19/17)ʸ=a(17/19)ʸ is b = ln(a) / ln(19/17), achieved by taking the natural logarithm of both sides and simplifying.
Step-by-step explanation:
The given equation (19/17)ʸ=a(17/19)ʸ can be rewritten in logarithmic form by applying the property of logarithms that states the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of these two numbers. Taking the natural logarithm (ln) of both sides of the equation, we get:
ln((19/17)ʸ) = ln(a(17/19)ʸ).
Because the powers on both sides of the equation are the same, we can remove them from the logarithm as a factor:
b × ln(19/17) = b × ln(a) + b × ln(17/19).
Now, simplify to isolate the unknown variable 'b' by dividing both sides by the factor that includes 'b' to obtain:
ln(19/17) = ln(a) + ln(17/19).
Lastly, we can simplify further by recognizing that ln(17/19) is the negative of ln(19/17), thus the equation simplifies to:
b = ln(a) / ln(19/17).
So the logarithmic form of the given equation is:
b = ln(a) / ln(19/17).