5log2+3/2log25+1/2log49-log28
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Assume that all logarithms are with respect to the same .
Y = 5 log 2 + 3/2 log 25 + 1/2 log 49 – log 28
We know log x + log y = log x y rule 1 and n log x = x^n rule 2 Apply rule 1 on each of the four terms on RHS .
Y = log 25 + log (5²2)3/2 + log (7²2)1/2 - log 7*2²2 Now apply 1st rule
= log 2^5 * (5²)^3/2 * (7²2)^1/2 / 7*2² = log 2^5 * 5^3 * 7 * 7^-1 * 2^-2
= log 8 * 125 = log 1000 = 3
Y = 5 log 2 + 3/2 log 25 + 1/2 log 49 – log 28
We know log x + log y = log x y rule 1 and n log x = x^n rule 2 Apply rule 1 on each of the four terms on RHS .
Y = log 25 + log (5²2)3/2 + log (7²2)1/2 - log 7*2²2 Now apply 1st rule
= log 2^5 * (5²)^3/2 * (7²2)^1/2 / 7*2² = log 2^5 * 5^3 * 7 * 7^-1 * 2^-2
= log 8 * 125 = log 1000 = 3
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4
Answer:
the answer of 5 log 2 +3/2 log 25 +1/2 log 49 –log 28 is 3
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