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Given that log102 = x and log103 = y, the value of log1060 is expressed as?
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Given that log102 = x and log103 = y, the value of log1060 is expresse...
Calculating log1060 given log102 = x and log103 = y
Understanding logarithms
Logarithms are mathematical functions that help us solve problems involving exponents or powers. The logarithm of a number to a given base is the exponent to which the base must be raised to obtain that number. For example, if we take a base of 10 and find the logarithm of 100, we get 2 because 10 raised to the power of 2 gives us 100.
Using logarithm rules
There are certain rules that we can apply when working with logarithms. One of these is the product rule, which states that the logarithm of a product is equal to the sum of the logarithms of the individual factors. For example, log10(2x) = log10(2) + log10(x).
Solving for log1060
Using the product rule, we can express 1060 as a product of powers of 2, 3, and 5:
- 1060 = 2^2 * 5 * 3^3
- log10(1060) = log10(2^2 * 5 * 3^3)
- log10(1060) = log10(2^2) + log10(5) + log10(3^3)
- log10(1060) = 2log10(2) + log10(5) + 3log10(3)
Now we can substitute the given values of x and y for log10(2) and log10(3), respectively:
- log10(1060) = 2x + log10(5) + 3y
- log10(1060) = 2log102 + log103 + 3log103
- log10(1060) = 2x + y + 3y
- log10(1060) = 2x + 4y
Therefore, the value of log1060 is 2x + 4y.
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Given that log102 = x and log103 = y, the value of log1060 is expressed as?
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Given that log102 = x and log103 = y, the value of log1060 is expressed as? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Given that log102 = x and log103 = y, the value of log1060 is expressed as? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that log102 = x and log103 = y, the value of log1060 is expressed as?.
Given that log102 = x and log103 = y, the value of log1060 is expressed as? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Given that log102 = x and log103 = y, the value of log1060 is expressed as? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Given that log102 = x and log103 = y, the value of log1060 is expressed as?.
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