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

Sagot :

Answer:

[tex]x=\frac{1}{4}[/tex]

Step-by-step explanation:

Given:

[tex]2log(\frac{2}{3})=\frac{1}{2}log(x)-log(18)+log(16)[/tex]

Use the Power Rule Law:

[tex]log(\frac{2}{3}^2)=log(x^{1/2})+log(16)-log(18)[/tex]

Use the Quotient Rule Law:

[tex]log(\frac{4}{9})=log(\sqrt{x})+log(\frac{16}{18})[/tex]

Use the Product Rule Law:

[tex]log(\frac{4}{9})=log(\frac{16\sqrt{x}}{18})[/tex]

Simplify:

[tex]log(\frac{4}{9})=log(\frac{8\sqrt{x}}{9})[/tex]

[tex]\frac{4}{9}=\frac{8\sqrt{x}}{9}[/tex]

[tex]4=8\sqrt{x}[/tex]

[tex]\frac{4}{8}=\sqrt{x}[/tex]

[tex]\frac{1}{2}=\sqrt{x}[/tex]

[tex]\frac{1}{4}=x[/tex]

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