Question

高一数学,log5^3=a,log5^2=b,用a、b表示,log1.5^2.4

Answer 1

换底公式

log1.5^2.4

=log5^2.4/log5^1.5

=(log5^12-log5^5)/(log5^3-log5^2)

=(log5^(3*4)-log5^5)/(log5^3-log5^2)

=(log5^3+log5^4-log5^5)/(log5^3-log5^2)

=(log5^3+2log5^2-log5^5)/(log5^3-log5^2)

=(a+2b-1)/(a-b)