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zvonat [6]
2 years ago
14

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

Mathematics
1 answer:
sweet-ann [11.9K]2 years ago
5 0

Answer:

x=\frac{1}{4}

Step-by-step explanation:

<u>Given:</u>

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

<u>Use the Power Rule Law:</u>

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

<u>Use the Quotient Rule Law:</u>

log(\frac{4}{9})=log(\sqrt{x})+log(\frac{16}{18})

<u>Use the Product Rule Law:</u>

log(\frac{4}{9})=log(\frac{16\sqrt{x}}{18})

<u>Simplify:</u>

log(\frac{4}{9})=log(\frac{8\sqrt{x}}{9})

\frac{4}{9}=\frac{8\sqrt{x}}{9}

4=8\sqrt{x}

\frac{4}{8}=\sqrt{x}

\frac{1}{2}=\sqrt{x}

\frac{1}{4}=x

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