jika ³log2 = a dan ²log 7 = b  maka ¹⁴ log 81 = ....?

[tex]^{3}log_{2} = a \\ ^{2}log_{7} = b \\ ^{14}log_{81} = ...[/tex]
Penyelesaian :

[tex]= \frac{^{2}log_{81}}{^{2}log_{14}} \\ = \frac{^{2}log_{(9*9)}}{^{2}log_{7*2}} \\ = \frac{^{2}log_{(3^{2}*3^{2})}}{^{2}log_{7+^{2}log{2}}} \\ = \frac{^{2}log_{3^{2}}^{2}+^{2}log_{3^{2}}}{^{2}log_{7+^{2}log{2}}} \\ = \frac{2.^{2}log_{3}+2.^{2}log_{3}}{^{2}log_{7+^{2}log{2}}} \\ = \frac{2.(1/a)+2.(1/a)}{b+1} \\ = \frac{2/a+2/a}{b+1} [/tex]

Setelah itu Kalikan a/a :

[tex]= \frac{a}{a} *\frac{2/a+2/a}{b+1}[/tex]

[tex]= \frac{2a/a+2a/a}{ab+a}[/tex]

[tex]= \frac{2+2}{ab+a}[/tex]

[tex]= \frac{4}{ab+a}[/tex]

³log2 = a
²log7 = b

= ¹⁴log81
= ¹⁴log3₄
= 4¹⁴log3
= 4 / ³log14
= 4 / ³log2 x ³log7
= 4 / a x ab
= 4 / a(1 x b)