Question

show that log 27540 =2log2 +4log3 +log5 +log17

Answer 1

You can solve it by applying the rule that says
log mn = log m + log n
So,
2Log 2+4log 3+log 5+log 17
=log 2^2 + log 3^4 + log 5 + log 17
= log 4 +log 81 +log 5 +log 17
=log (4x81x5x17)
=log 27540

Hope it will help...
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Answer 2

Answer:

log27540

Step-by-step explanation:

Given:

log 27540=2 log 2+4 log3 +log5+log17

To prove:

log 27540=2 log 2+4 log3 +log5+log17

Solution:

Since the given logarithmic term influences the entire question, attention should be taken while creating equations from it. Additionally, calculations for these types of questions must be done with extreme precision and concentration because even a small error might cause the entire answer to be incorrect .We must identify the terms in charge of the portion prior to the decimals. Then, we attempt to make it a power of 10. With base 10, we apply many logarithm laws. We discover a number of terms in the expansion of 10 with its distinct power number at the conclusion, which provides the answer.

Solving the RHS

$=log2^{2}+log3^{4} +log5+log17\\=log4+log81+log5+log17$

=log(4×81×5×7)

=log27540

Thus LHS=RHS

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