solve-for-x-the-following-equations-a-log-x-3-2log-x-2-2log-x-2log-x-3-b-log-x-24-3log-x-4-2log-x-3-3-

Question Number 68618 by Rio Michael last updated on 14/Sep/19

s o l v e f o r x t h e f o l l o w i n g e q u a t i o n s

a) l o g x^{3} - 2 l o g x^{2} + 2 l o g x + 2 l o g \sqrt{x} = 3

b) {l o g}_{x} 24 - 3 {l o g}_{x} 4 + 2 {l o g}_{x} 3 = - 3

Answered by Rasheed.Sindhi last updated on 14/Sep/19

a) l o g x^{3} - 2 l o g x^{2} + 2 l o g x + 2 l o g \sqrt{x} = 3

b) {l o g}_{x} 24 - 3 {l o g}_{x} 4 + 2 {l o g}_{x} 3 = - 3

a) \Rightarrow 3 \log x - 4 logx + 2 logx + logx = 3

2 \log x = 3

x = Antilog (\frac{3}{2}) = 10^{\frac{3}{2}} = \sqrt{1000} = 10 \sqrt{10}

b) {l o g}_{x} 24 - 3 {l o g}_{x} 4 + 2 {l o g}_{x} 3 = - 3

\log_{x} 24 - \log_{x} 4^{3} + \log_{x} 3^{2} = - 3

\log_{x} (\frac{24 \times 9}{64}) = - 3

\log_{x} (\frac{27}{8}) = - 3

x^{- 3} = \frac{27}{8} = {(\frac{3}{2})}^{3} = {(\frac{2}{3})}^{- 3}

x = \frac{2}{3}

Commented by Rio Michael last updated on 15/Sep/19

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