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
I have given up on the question
I'm sorry to hear that you have given up on the question. If you have any other questions or need further assistance in the future, feel free to ask.
Thanks I love this I will introduce my friends to this
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The second and fifth term of go are 1 and 1/8 find the common ratio and the first and right term
To find the common ratio and the first and ninth term of a geometric sequence (denoted as a, ar, ar^2, ar^3, ..., ar^(n-1)), we can use the given information.
Here, the second term (ar) is 1 and the fifth term (ar^4) is 1/8.
From the given information, we can set up the following equations:
ar = 1 (Equation 1)
ar^4 = 1/8 (Equation 2)
To find the common ratio (r), we can divide Equation 2 by Equation 1:
(ar^4) / (ar) = (1/8) / (1)
r^(4-1) = 1/8
r^3 = 1/8
r = (1/8)^(1/3)
r = 1/2
So, the common ratio is 1/2.
Substituting the value of r into Equation 1 (ar = 1), we can solve for the first term (a):
(a * (1/2)) = 1
a = 2
Therefore, the first term (a) is 2, and the common ratio (r) is 1/2.
To find the ninth term, we can use the formula for the nth term of a geometric sequence:
ar^(n-1)
Substituting the values of a (2), r (1/2), and n (9) into the formula, we have:
2 * (1/2)^(9-1)
2 * (1/2)^8
2 * (1/256)
1/128
Therefore, the ninth term of the sequence is 1/128.