Pertanyaan

Bentuk sederhana dari 7 lo g 15 16 + 5 lo g 24 25 + 3 lo g 80 81 adalah ....

Bentuk sederhana dari $7 lo g \frac{16}{15} + 5 lo g \frac{25}{24} + 3 lo g \frac{81}{80}$ adalah ....

log 5
log 3
log 2
- log 2

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$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 7 log invisible function application 16 over 15 end cell equals cell log invisible function application open parentheses 16 over 15 close parentheses to the power of 7 semicolon italic m middle dot log invisible function application italic b equals log invisible function application italic b to the power of italic m end cell row blank equals cell log invisible function application open parentheses fraction numerator italic 2 to the power of italic 4 over denominator italic 3 italic middle dot italic 5 end fraction close parentheses to the power of italic 7 end cell row blank equals cell log invisible function application fraction numerator 2 to the power of 28 over denominator 3 to the power of 7 middle dot 5 to the power of 7 end fraction end cell row blank blank blank row cell 5 log invisible function application 25 over 24 end cell equals cell log invisible function application open parentheses 25 over 24 close parentheses to the power of 5 semicolon italic m middle dot log invisible function application italic b equals log invisible function application italic b to the power of italic m end cell row blank equals cell log invisible function application open parentheses fraction numerator italic 5 to the power of italic 2 over denominator italic 2 to the power of italic 3 italic middle dot italic 3 end fraction close parentheses to the power of italic 5 end cell row blank equals cell log invisible function application fraction numerator 5 to the power of 10 over denominator 2 to the power of 15 middle dot 3 to the power of 5 end fraction end cell row blank blank blank row cell 3 log invisible function application 81 over 80 end cell equals cell log invisible function application open parentheses 81 over 80 close parentheses cubed semicolon italic m middle dot log invisible function application italic b equals log invisible function application italic b to the power of italic m end cell row blank equals cell log invisible function application open parentheses fraction numerator italic 3 to the power of italic 4 over denominator italic 2 to the power of italic 4 italic middle dot italic 5 end fraction close parentheses to the power of italic 3 end cell row blank equals cell log invisible function application fraction numerator 3 to the power of 12 over denominator 2 to the power of 12 middle dot 5 cubed end fraction end cell end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 7 log invisible function application 16 over 15 plus 5 log invisible function application 25 over 24 plus 3 log invisible function application 81 over 80 end cell equals cell log invisible function application fraction numerator 2 to the power of 28 over denominator 3 to the power of 7 middle dot 5 to the power of 7 end fraction plus log invisible function application fraction numerator 5 to the power of 10 over denominator 2 to the power of 15 middle dot 3 to the power of 5 end fraction plus log invisible function application fraction numerator 3 to the power of 12 over denominator 2 to the power of 12 middle dot 5 cubed end fraction end cell row blank equals cell log invisible function application fraction numerator 2 to the power of 28 over denominator 3 to the power of 7 middle dot 5 to the power of 7 end fraction middle dot fraction numerator 5 to the power of 10 over denominator 2 to the power of 15 middle dot 3 to the power of 5 end fraction middle dot fraction numerator 3 to the power of 12 over denominator 2 to the power of 12 middle dot 5 cubed end fraction end cell row blank equals cell log invisible function application fraction numerator 2 to the power of 28 middle dot 3 to the power of 12 middle dot 5 to the power of 10 over denominator 2 to the power of 27 middle dot 3 to the power of 12 middle dot 5 to the power of 10 end fraction end cell row blank equals cell log invisible function application 2 end cell end table end style$