Simplify log 10(30/16)-2 log (5/9)+log 10(400/243)
All of these logs are base 10, so we can take advantage of the log properties to simplify this question.
log(PQ) = logP + logQ,
log(P/Q) = logP - logQ,
and log(P^N) = NlogP.
Substituting these properties into the given expression:
log10(30/16) - 2log10(5/9) + log10(400/243)
= log10(30) - log10(16) - 2(log10(5) - log10(9)) + log10(400) - log10(243)
= log10(30) + log10(9^2) - log10(16) + log10(5^2) + log10(400) - log10(243)
= log10(30) + 2log10(9) - log10(16) + 2log10(5) + log10(400) - log10(243)
= log10(30*9^2*5^2*400) - log10(16*243)
= log10[(30*81*25*400)/(16*243)]
= log10[24300000/3888].
Now this can be simplified:
= log10[6250]
= 4.792.
So the simplified form of the expression is 4.792.
I don't understand the answer
I apologize for the confusion. Let's go through the simplification process step by step:
log10(30/16) - 2log10(5/9) + log10(400/243)
= log10(30) - log10(16) - 2(log10(5) - log10(9)) + log10(400) - log10(243)
= log10(30) - log10(16) - 2log10(5) + 2log10(9) + log10(400) - log10(243)
Using log properties, we can simplify further:
= log10(30) - log10(16) - log10(5^2) + log10(9^2) + log10(400) - log10(243)
= log10(30) - log10(16) - log10(25) + log10(81) + log10(400) - log10(243)
Now, we can combine the logarithms using the properties mentioned earlier:
= log10((30 * 81 * 400) / (16 * 25 * 243))
= log10(972000 / 97200)
= log10(10)
= 1
Therefore, the simplified expression is equal to 1.
Too long please make it short
Apologies for the lengthy explanation. Here is the simplified expression:
log10(30/16) - 2log10(5/9) + log10(400/243) = 1
I don't mean you just give me the answer , solve it but make it short
log10(30/16) - 2log10(5/9) + log10(400/243)
= log10[(30/16) * (400/243)^2]
= log10[(30 * 400 * 400)/(16 * 243 * 243)]
= log10[16000000/944784]
= log10(16.929)
= 1.228
Please my brain can't carry this
answers
I apologize for the confusion. Here are the simplified answers for each term:
log10(30/16) simplifies to log10(1.875)
2log10(5/9) simplifies to log10((5/9)^2)
log10(400/243) simplifies to log10(1.646)
Now, using a calculator or logarithm table, you can find the values for each simplified term:
log10(1.875) ≈ 0.273
log10((5/9)^2) ≈ -0.196
log10(1.646) ≈ 0.216
Finally, add up these values:
0.273 - 2(-0.196) + 0.216 ≈ 0.973