\(\Leftrightarrow25^{f\left(x\right)}-125.5^{f\left(x\right)}-m.5^{f\left(x\right)}+125m=0\)
\(\Leftrightarrow5^{f\left(x\right)}.\left(5^{f\left(x\right)}-125\right)-m.\left(5^{f\left(x\right)}-125\right)=0\)
\(\Leftrightarrow\left(5^{f\left(x\right)}-125\right)\left(5^{f\left(x\right)}-m\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5^{f\left(x\right)}=125\\5^{f\left(x\right)}=m\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}f\left(x\right)=3\\f\left(x\right)=log_5m\end{matrix}\right.\)
Pt \(f\left(x\right)=3\) có 2 nghiệm
\(\Rightarrow f\left(x\right)=log_5m\) có 3 nghiệm
\(\Rightarrow-1< log_5m< 3\)
\(\Rightarrow\dfrac{1}{5}< m< 125\)
Có 124 giá trị nguyên dương
