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Without using logarithm tables, find the value of x given that: 2log2/3 = 1/2logx - log 18 + log 16

1 Answer

10 votes

Answer:


x=(1)/(4)

Explanation:

Given:


2log((2)/(3))=(1)/(2)log(x)-log(18)+log(16)

Use the Power Rule Law:


log((2)/(3)^2)=log(x^(1/2))+log(16)-log(18)

Use the Quotient Rule Law:


log((4)/(9))=log(√(x))+log((16)/(18))

Use the Product Rule Law:


log((4)/(9))=log((16√(x))/(18))

Simplify:


log((4)/(9))=log((8√(x))/(9))


(4)/(9)=(8√(x))/(9)


4=8√(x)


(4)/(8)=√(x)


(1)/(2)=√(x)


(1)/(4)=x

User Nakilon
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