Question

Express log(12 under root a power 5 b power 7 c power 9) in terms of log a log b log c

Answer 1

Answer:

598 is your answer

Step-by-step explanation:

I hope it helps

Answer 2

Given,

$\[\log \left( {12\sqrt {{a^5}{b^7}{c^9}} } \right)\]$

Solution,

$\[ = \log \left( {12\sqrt {{a^5}{b^7}{c^9}} } \right)\]$

$\[ = \log 12 + \log {\left( {{a^5}{b^7}{c^9}} \right)^{\frac{1}{2}}}\]$

$\[ = \log 12 + \frac{1}{2}\log \left( {{a^5}{b^7}{c^9}} \right)\]$

$\[ = \log 12 + \frac{1}{2}\left( {\log {a^5} + \log {b^7} + \log {c^9}} \right)\]$

$\[ = \log 12 + \frac{1}{2}\left( {5\log a + 7\log b + 9\log c} \right)\]$

$\[ = \log 12 + \frac{5}{2}\log a + \frac{7}{2}\log b + \frac{9}{2}\log c\]$

Hence the expression is $\[\log 12 + \frac{5}{2}\log a + \frac{7}{2}\log b + \frac{9}{2}\log c\]$.