find the value of log√27 +log 8+log√1000 by(means divided by)/log 120? pls ans some questions wt iam asking after I need help tenn.
Answers
Answer:
log(3
3
)+log(2
3
)+
2
1
log(10
3
)
= \frac{\frac{3}{2} \log3 + 3 \log(2) + \frac{3}{2} \log(10)}{\log(2^3)+\log3+ \log 5}
log(2
3
)+log3+log5
2
3
log3+3log(2)+
2
3
log(10)
= \frac{\frac{3}{2} \log3 + 3 \log(2) + \frac{3}{2} \log(2 \times 5)}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+3log(2)+
2
3
log(2×5)
= \frac{\frac{3}{2} \log3 + 3 \log2 + \frac{3}{2} (\log2 + \log 5)}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+3log2+
2
3
(log2+log5)
= \frac{\frac{3}{2} \log3 + 3 \log2 + \frac{3}{2} \log2 +\frac{3}{2} \log 5}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+3log2+
2
3
log2+
2
3
log5
= \frac{\frac{3}{2} \log3 + \frac{9}{2} \log2 +\frac{3}{2} \log 5}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+
2
9
log2+
2
3
log5
= \frac{3}{2}\frac{( \log3 + 3 \log2 + \log 5)}{3 \log2+\log3+ \log 5}
2
3
3log2+log3+log5
(log3+3log2+log5)
= \frac{3}{2}
2
3
Step-by-step explanation:
log(3
3
)+log(2
3
)+
2
1
log(10
3
)
= \frac{\frac{3}{2} \log3 + 3 \log(2) + \frac{3}{2} \log(10)}{\log(2^3)+\log3+ \log 5}
log(2
3
)+log3+log5
2
3
log3+3log(2)+
2
3
log(10)
= \frac{\frac{3}{2} \log3 + 3 \log(2) + \frac{3}{2} \log(2 \times 5)}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+3log(2)+
2
3
log(2×5)
= \frac{\frac{3}{2} \log3 + 3 \log2 + \frac{3}{2} (\log2 + \log 5)}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+3log2+
2
3
(log2+log5)
= \frac{\frac{3}{2} \log3 + 3 \log2 + \frac{3}{2} \log2 +\frac{3}{2} \log 5}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+3log2+
2
3
log2+
2
3
log5
= \frac{\frac{3}{2} \log3 + \frac{9}{2} \log2 +\frac{3}{2} \log 5}{3 \log2+\log3+ \log 5}
3log2+log3+log5
2
3
log3+
2
9
log2+
2
3
log5
= \frac{3}{2}\frac{( \log3 + 3 \log2 + \log 5)}{3 \log2+\log3+ \log 5}
2
3
3log2+log3+log5
(log3+3log2+log5)
= \frac{3}{2}
2
3
Answer:
3/2 is the answer for the given problem
answer is given in two types
