已知以三为底的5的对数=a,5的b次方=7,用a,b的代数式表示以63为底的105的对数

Question

已知以三为底的5的对数=a,5的b次方=7,用a,b的代数式表示以63为底的105的对数

Answer 1

∵log3(5)=a,∴a=lg5/lg3,∴1/a = lg3/lg5
∵5^b=7,∴b=log5(7) = lg7/lg5
log63(105) = lg105/lg63
= lg(3 * 5 * 7)/lg(3^2 * 7)
= (lg3+lg5+lg7)/(2lg3+lg7)
= (lg3/lg5+1+lg7/lg5)/(2lg3/lg5+lg7/lg5)
= (1/a+1+b)/(2/a+b)
= (1+a+ab)/(2+ab)