Pertanyaan

Nilai x yang memenuhi pertidaksamaan ( 81 ) x − 2 < ( ( 27 ) x ) ( 3 ( 9 ) 6 x ) adalah ....

Nilai $x$ yang memenuhi pertidaksamaan $(81)^{x - 2} < ((27)^{x}) (3 (9)^{6 x})$ adalah ....

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai yang memenuhi pertidaksamaan adalah .

nilai

yang memenuhi pertidaksamaan begin mathsize 14px style square root of open parentheses 81 close parentheses to the power of x minus 2 end exponent end root less than open parentheses square root of open parentheses 27 close parentheses to the power of x end root close parentheses open parentheses cube root of open parentheses 9 close parentheses to the power of 6 x end exponent end root close parentheses end style

begin mathsize 14px style square root of open parentheses 81 close parentheses to the power of x minus 2 end exponent end root less than open parentheses square root of open parentheses 27 close parentheses to the power of x end root close parentheses open parentheses cube root of open parentheses 9 close parentheses to the power of 6 x end exponent end root close parentheses end style

adalah

begin mathsize 14px style x greater than negative 8 over 7 end style

Pembahasan

Perhatikan Jadi, nilai yang memenuhi pertidaksamaan adalah .

Perhatikan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of left parenthesis 81 right parenthesis to the power of x minus 2 end exponent end root less than left parenthesis square root of left parenthesis 27 right parenthesis to the power of x end root right parenthesis left parenthesis cube root of open parentheses 9 close parentheses to the power of 6 x end exponent end root right parenthesis end cell row cell 3 to the power of 4 fraction numerator left parenthesis x minus 2 right parenthesis over denominator 2 end fraction end exponent end cell less than cell 3 to the power of fraction numerator 3 x over denominator 2 end fraction end exponent times 3 to the power of fraction numerator 12 x over denominator 3 end fraction end exponent end cell row cell 3 to the power of 2 x minus 4 end exponent end cell less than cell 3 to the power of fraction numerator 9 x plus 24 x over denominator 6 end fraction end exponent end cell row cell 3 to the power of 2 x minus 4 end exponent end cell less than cell 3 to the power of fraction numerator 33 x over denominator 6 end fraction end exponent end cell row cell 2 x minus 4 end cell less than cell fraction numerator 33 x over denominator 6 end fraction end cell row blank blank blank row cell 2 x minus fraction numerator 33 x over denominator 6 end fraction end cell less than 4 row cell fraction numerator 12 x minus 33 x over denominator 6 end fraction end cell less than 4 row cell fraction numerator negative 21 x over denominator 6 end fraction end cell less than 4 row cell negative 21 x end cell less than 24 row x greater than cell negative 8 over 7 end cell end table end style$

Jadi, nilai yang memenuhi pertidaksamaan begin mathsize 14px style square root of open parentheses 81 close parentheses to the power of x minus 2 end exponent end root less than open parentheses square root of open parentheses 27 close parentheses to the power of x end root close parentheses open parentheses cube root of open parentheses 9 close parentheses to the power of 6 x end exponent end root close parentheses end style adalah begin mathsize 14px style x greater than negative 8 over 7 end style .