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If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =?
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If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =?
Given Information:
a = log2x
b = log3(2x)
c = log3x
Calculation:
To find the value of abc, we need to substitute the given values of a, b, and c into the expression and simplify.
Step 1: Simplifying a
a = log2x
Using the property of logarithms, we can rewrite this as:
a = log2(x^1)
Using the exponent property of logarithms, we can further simplify this to:
a = 1 * log2(x)
Since log2(2) = 1, we can simplify this to:
a = log2(x)
Step 2: Simplifying b
b = log3(2x)
Using the property of logarithms, we can rewrite this as:
b = log3(2) + log3(x)
Using the change of base formula, we can rewrite log3(2) as log2(2) / log2(3):
b = (log2(2) / log2(3)) + log3(x)
Since log2(2) = 1, we can simplify this to:
b = (1 / log2(3)) + log3(x)
Step 3: Simplifying c
c = log3x
Using the property of logarithms, we can rewrite this as:
c = log3(x^1)
Using the exponent property of logarithms, we can further simplify this to:
c = 1 * log3(x)
Since log3(3) = 1, we can simplify this to:
c = log3(x)
Step 4: Substitute values into abc
abc = (log2(x)) * ((1 / log2(3)) + log3(x)) * (log3(x))
Using the associative property of multiplication, we can rearrange the terms:
abc = (log2(x) * 1 / log2(3) * log3(x)) * log3(x)
Combining the logarithmic terms, we can simplify this to:
abc = (log2(x) / log2(3)) * (log3(x))^2
Step 5: Final Simplification
To further simplify the expression, we can use the change of base formula to rewrite log2(x) as log10(x) / log10(2) and log3(x) as log10(x) / log10(3):
abc = (log10(x) / log10(2)) * (log10(x) / log10(3))^2
Simplifying the expression, we get:
abc = (log10
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If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =?
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If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =? 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 If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =?.
If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =? 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 If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a = log2x x b=log 3 ,2x ; c=log.,3x, then the value of abc 1 =?.
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