> plot(exp(x),x=-1..1); > plot(0.1^x,x=-1..1);The logarithmic function was introduced for as the inverse of the exponential. The logarithm is therefore inreasing if and decreasing if . Indeed you can plot and .
> plot(log(x),x=0.1..10); > plot(log[0.1](x),x=0.1..10);From the monotonicity properties you can compare two logarithms having the same base without computing their values:
> with(plots): > animate(log[b](x),x=0.1..10,b=1.1..10,frames=30); > animate(log[b](x),x=0.1..10,b=0.01..0.1,frames=30);From the monotonicuty properties you can see that for a fixed in the interval the logarithm increases with but for in the interval it decreases. As a result you can now compare logarithms with different bases without computing their values.
> solve(5^(x+1)+5^x+5^(x-1)=155,x); > simplify(%);Note: The % calls up the last command entered
> solve(log[sqrt(x-1)](2*x^2+2*x+5)=4,x); > evalf(%);