Diketahui operasi bentuk logaritma dibawah ini, tentukan nilai x yang memenuhi jika nilai x tersebut.... Question from @Anthology

May 2022 2 70 Report

Diketahui operasi bentuk logaritma dibawah ini, tentukan nilai x yang memenuhi jika nilai x tersebut merupakan penyelesaian untuk a.
[tex]x = \tt \frac{ {}^{4}log \: 64 + {}^{3} log \: 27 - {}^{2}log \: 128 }{log \: 100} \\ [/tex]
Maka, tentukan hasil dari [tex] \tt f(a) = 2 {a}^{2} + 3a [/tex].

Note: Dilarang asal-asalan.

EIderberry

》Logaritma

$\:$

$\begin{gathered}\begin{gathered}\begin{aligned} \sf x &=\sf \frac{4 \: log \: 64 + 3 \: log \: 27 - 2 \: log \: 128}{log \: 100} \ \\ \sf x&=\sf \frac{4 \: log \: {4}^{3} + 3 \: log \: {3}^{3} - 2 \: log \: {2}^{7} }{log \: {10}^{2} } \\ \sf x&= \sf \frac{3 + 3 - 7}{2} \\ \sf x&= \sf - \frac{1}{2} \\ \end{aligned}\end{gathered}\end{gathered}$

Substitusikan Penyelesaian a

$\begin{gathered}\begin{gathered}\begin{aligned} \sf f(a) &=\sf 2 {a}^{2} + 3a\\ \sf f( - \frac{1}{2} )&=\sf 2( - \frac{1}{2} ){}^{2} + 3( - \frac{1}{2}) \\ \sf f( - \frac{1}{2}) &= \sf 2 \times \frac{1}{4} + ( - \frac{3}{2} )\\ \sf f( - \frac{1}{2} )&= \sf \frac{2}{4} - \frac{3}{2} \\ \sf f( - \frac{1}{2} )&= \sf - 1 \end{aligned}\end{gathered}\end{gathered}$

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XxDarknessxX

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9 votes Thanks 5

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