Question

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

Answer 1

`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`