Question

write 2 log 3+3 log 5-5 log 2 as a single logarithum​

Answer 1

Hey, here is your answer.......

2log3 + 3log5 - 5log2.

2log3 = log$3^{2}$ = log9

3log5 = log$5^{3}$ = log125

5log2 = log$2^{5}$ = log32


Then,

2log3 + 3log5- 5log2 = log9 + log125 - log32

log9 + log125 = log(9)(125) = log(1125) [since, log a + log b = log (ab)]

log(1125) - log(32) = log(1125/32) [since, log c - log d = log (c/d)]


Therefore, log9 + log125 - log32 = log(1125/32)

i.e., 2log3 + 3log5 - 5log2 = log(1125/32)





Hope this helps you.......
Thank you........


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