What is the minimum value of
$$\log_a(x)+ \log_x(x) $$
where $0\leq a\leq x.$ I do not understand why my book says the answer is $2$ because when i take $a=0.1$ say and $x =0.2$ I get $\approx 1.6$....
So is my book wrong or am i wrong?
2026-05-15 01:12:53.1778807573
Minimum value of a Logarithmic equation
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Well $$ \log_x(x)=1 $$ So the function is $$ \log_a(x)+1 $$ Since $\log_a(x)$ has a limit of $-\infty$ when approaching either $0$ or $\infty$ depending on the value of $a$, there is no minimum.