Question

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. pls help waiting for answer​

Answer 1

Answer:

Expansion of Expressing with the Help of the Laws of Logarithm

Step-by-step explanation:

$\frac{ log\sqrt{27 } + log8 + log \sqrt{1000} }{ log120 }$

$= \frac{ log(27) {}^{ \frac{1}{2} } + log {2}^{3} + log {1000}^{ \frac{1}{2} } }{ log(3 \times {2}^{2} \times 10)}$

$= \frac{ log(3) {}^{3 \times \frac{1}{2} } + log2 {}^{3} + log(10) {}^{3 \times \frac{1}{2} } }{ log3 + log {2}^{2} + log10 }$

$= \frac{ \frac{3}{2} log3 + 3 log2 + \frac{3}{2} log(10) }{ log3 + 2 log2 + log10 }$

$= \frac{ \frac{3}{2} log3 + \frac{3}{2} (2 log2) + \frac{3}{2} (1) }{ log3 + 2 log2 + 1 }$

$= \frac{ \frac{3}{2}( log3 + 2 log2 + 1) }{ log3 + 2 \: log \: 2 + 1 }$

$= \frac{3}{2}$