The required answer of the expression 9log9(4) = 14.
What are logarithmic proerties?
The property include product, quotient, and power rules of logarithms. They are very helpful in expanding or compressing logarithms.
Now the given expression is
9log9(4)
Using the logarithmic property,
log(mn) = logm + logn
So,
9log9(4) = 9[log9 + log4]
since, 3² = 9
and 2² = 4
therefore we can write,
9log9(4) = 9[log3² + log2²]
Using logarithmic property,
logmⁿ = nlogm
So,
log3² = 2log3
log2² = 2log2
Hence,
9log9(4) = 9[2log3 + 2log2]
Since log3 = 0.4771
and log2 = 0.3010
⇒9log9(4) = 9[2*0.4771 + 2*0.3010]
⇒9log9(4) = 9[ 0.9542 + 0.6020]
⇒9log9(4) = 9*1.5562
⇒9log9(4) = 14
Hence,The required answer of the expression 9log9(4) = 14.
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