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5 votes
5 votes
Let u = In a and v= In b. Write the expression in terms of u and v without using the logarithm function. In (b6.5√a)​

User Broguyman
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1 Answer

6 votes
6 votes

Answer:

6.5v +0.5u

Explanation:

You want to express ln(b^6.5·√a) in terms of u = ln(a) and v = ln(b).

Rules of logarithms

The relevant rules of logarithms are ...

ln(ab) = ln(a)+ln(b)

ln(a^b) = b·ln(a)

Application

The given logarithm can be rewritten as ...

ln(b^6.5·√a) = ln(b^6.5) +ln(a^0.5) = 6.5ln(b) +0.5ln(a)

= 6.5v +0.5u

User Chris Hill
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