so sanh 4^17 va 5^15 giai thichthat ro rangminh se vote 5 sao luon nhung phai dung nhe
so sanh 4^17 va 5^15 giai thichthat ro rangminh se vote 5 sao luon nhung phai dung nhe
By Aubrey
By Aubrey
so sanh 4^17 va 5^15 giai thichthat ro rangminh se vote 5 sao luon nhung phai dung nhe
Đáp án:
\({5^{15}} > {4^{17}}.\)
Giải thích các bước giải:
\(\begin{array}{*{20}{l}}
{{4^{17}},{\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {5^{15}}}\\
{{5^{15}} < {6^{15}} = {2^{15}}{{.3}^{15}}}\\
{{4^{17}} = {{\left( {{2^2}} \right)}^{17}} = {2^{17}}{{.2}^{17}} = {2^{15}}{{.2}^{19}}}\\
{Ta{\kern 1pt} {\kern 1pt} co:{\kern 1pt} {\kern 1pt} \,\,\,{3^{15}}{\kern 1pt} {\kern 1pt} {\kern 1pt} > {\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} {2^{19}}}\\
{ \Rightarrow {2^{15}}{{.3}^{15}} > {2^{15}}{{.2}^{19}}}\\
{ \Rightarrow {5^{15}} > {2^{15}}{{.3}^{15}} > {2^{15}}{{.2}^{19}} = {4^{17}}}\\
{ \Rightarrow {5^{15}} > {4^{17}}.}
\end{array}\)
$\frac{4^{17}}{5^{15}}=\frac{4^{15}.4^{2}}{5^{15}}=16.(\frac{4}{5})^{15}=16.(0,8)^{15}<1$
$→ 4^{17}<5^{15}$