Ta có:
$24^{30}$ : $144^{n+1}$=$8^{10}$
⇔$24^{30}$ : $144^{n+1}$ : $8^{10}$=1
⇔$3^{30}$ . $8^{30}$ : $(12²)^{n+1}$ : $8^{10}$ =1
⇔$3^{30}$ . $2^{90}$ : $12^{2n+2}$ : $2^{30}$ = 1
⇔$3^{30}$ . $2^{60}$ : $12^{2n+2}$=1
⇔$3^{30}$ . $2^{60}$=$12^{2n+2}$
⇔$3^{30}$ . $2^{60}$=$12^{2n}$ . $2^{4}$ . $3^{2}$
⇔$3^{28}$ . $2^{56}$=$12^{2n}$
⇔$3^{28}$ . $4^{28}$=$12^{2n}$
⇔$12^{28}$=$12^{2n}$
⇔28=2n
⇔n=14.
Vậy n=14
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