# Write as a simplified logarithm: 6 (log c)/log a + 5 loga d - 7 loga b Note: The letter "a" in 5 loga d and -7 loga b is a small subscript "a" whereas the letter "a" in 6 log c / log a is a normal a.

## Expert Answers

We have to simplify : 6 (log c/log a) + 5 log(a) d - 7 log(a) b

Now we use the relation that log(a)b = log b / log a

6 (log c/log a) + 5 log(a) d - 7 log(a) b

=> 6(log c/ log a) + 5( log d/ log a) - 7(log b/ log a)

=> (1/ log a)[ 6 log c + 5 log d - 7 log b)

use log a  + log b = log (a*b) and a*log b = log (b^a)

=> (1/ log a)[ log c^6 + log d^5 - log b^7)

=>  (1/ log a)[ log c^6*d^5 / b^7)

Therefore the required result is (1/ log a)[ log (c^6*d^5 / b^7)]

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