Question

if log 7 - log 2 + log 16 - 2 log 3 - log 7/ 45 =1 + log n. find n​

Answer 1

Step-by-step explanation:

Given:-

log 7 - log 2 + log 16-2 log 3 - log 7/45 =1 +log n.

To find:-

Find the value of n?

Solution:-

Given that

log 7 - log 2 + log 16-2 log 3 - log 7/45

=1 +log n.

We know that

log (a/b)=log a - log b

=> log7-log2+log16-2log3-(log7-log45)

=1+logn

=>log7-log2+log2^4-2log3-log7+log45

=1+log n

log7-log2+log2^4-2log3-log7+log(3^2×5)

=1+logn

We know that

log(ab)=log a + logb

log7-log2+log2^4-2log3-log7+log3^2

+log5=1+logn

we know that

log a^m = m log a

=>log7-log2+4log2-2log3-log7+2log3+

log5=1+logn

=>(log7-log7)+(-log2+4log2)+(-2log3+2log3) +log5=1+logn

=>0+3log2+0+log5=1+logn

=>3log2+log5=1+logn

=> log 2^3 + log 5 = 1+ log n

=> log 8 + log 5 = 1+log n

=> log (8×5) = 1+ log n

=> log 40 = 1+log n

=> log (10×4) = 1+ log n

=> log 10 + log 4 = 1+ log n

We know that log 10 (10) = 1

=> 1+ log 4 = 1 + log n

On Comparing both sides then

=> n = 4

Answer:-

The value of n for the given problem is 4

Used formulae:-

• log (ab)=log a + log b

• log (a/b)=log a - log b

• log (a^m)=m log a

• log a (a) = 1

• If base of the logarithm of a number is not given then the base is 10 and it is a common logarithm.