20. One day three planets were seen in the sky. One of them rotates about thesun in 87 days and the other two in 232 days and 1218 days. After howmany days will they again be seen simultaneously in the sky ?
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expansion of log120/49 is given below
Step-by-step explanation:
prime factorisation of 120= 2 ×2×2×3×5=2³ ×3×5
Prime Factorisation of 49 = 7×7= 7²
log 120/49= log120 -log49 as loga/b= log a-log b
=log 2³ ×3×5 - log 7²
= log 2³ + log 3+ log5 - log 7² as( log a×b= loga +log b)
=3log 2 +log3 + log 5 - 2log7 as( log a² = 2loga)
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★ Answer :
One day three planets were seen in the sky. One of them rotates about thesun in 87 days and the other two in 232 days and 1218 days. After howmany days will they again be seen simultaneously in the sky.
Taking L.C.M
→ 87 * 2 * 116 * 7
→ 1,41,228 days
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