Question

find the value
log(145/8) -3log 3/2 +log (54/29)​

Answer 1

Step-by-step explanation:

Given:-

log(145/8) -3log 3/2 +log (54/29)

To find:-

find the value of log(145/8) -3log 3/2 +log (54/29)

Solution:-

log(145/8) -3log (3/2 )+log (54/29)

We know that log(a/b)=log a- log b

=>(log 145-log8)-3(log3-log2)+(log54-log29)

=>log145-log8-3log2+3log2+log54-log29

=>log(29×5)-log2³-3log2+3log2+log(2×3³)-log29

we know that log(ab)=log a× log b

=>log29+log5-log2³-3log2+3log2+log2+log3³

-log29

we know that lpga^m=mloga

=>log29+log5-3log3-3log2+3log2+log2+3log3- log29

=>log5+log2

=>log(5×2)

=>log10

=>log10(10)

we know that loga(a)=1

=>1

Answer:-

The value of log(145/8) -3log 3/2 +log (54/29)=1

Used formulae:-

• log(ab)=log a+ log b
• log(a/b)=log a- log b
• log a^m=m log a
• log a to the base a=1
• If there is no base in the given logarithmic value then it is a common logarithm and its base is 10.

Answer 2

Step-by-step explanation:

Given:-

log(145/8) -3log 3/2 +log (54/29)

To find:-

find the value of log(145/8) -3log 3/2 +log (54/29)

Solution:-

log(145/8) -3log (3/2 )+log (54/29)

We know that log(a/b)=log a- log b

=>(log 145-log8)-3(log3-log2)+(log54-log29)

=>log145-log8-3log2+3log2+log54-log29

=>log(29×5)-log2³-3log2+3log2+log(2×3³)-log29

we know that log(ab)=log a× log b

=>log29+log5-log2³-3log2+3log2+log2+log3³

-log29

we know that lpga^m=mloga

=>log29+log5-3log3-3log2+3log2+log2+3log3- log29

=>log5+log2

=>log(5×2)

=>log10

=>log10(10)

we know that loga(a)=1

=>1

Answer:-

The value of log(145/8) -3log 3/2 +log (54/29)=1

Used formulae:-

log(ab)=log a+ log b

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

log a^m=m log a

log a to the base a=1

If there is no base in the given logarithmic value then it is a common logarithm and its base is 10.