CA Foundation Exam > CA Foundation Questions > If y = log_3(x) 3 logex, then dy/dx is :?
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If y = log_3(x) 3 logex, then dy/dx is :?
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If y = log_3(x) 3 logex, then dy/dx is :?
Solution:
Given, y = log_3(x) 3 log_e(x)
Let's solve this step by step.
Step 1: Simplify the given expression.
We know, log_a(b) = log_c(b) / log_c(a)
Applying this formula on the given expression, we get:
y = log_3(x) 3 log_e(x)
y = log_e(x) / log_e(3) 3 log_e(x)
y = (1 / log_e(3)) * log_e(x) log_e(x^3)
y = (1 / ln(3)) * ln(x) 3 ln(x)
y = [(1 / ln(3)) + 3] * ln(x)
Step 2: Differentiate both sides with respect to x.
We get,
dy/dx = [(1 / ln(3)) + 3] * d/dx(ln(x))
dy/dx = [(1 / ln(3)) + 3] * (1/x)
Step 3: Simplify the expression.
dy/dx = [(1 / ln(3)) + 3] * (1/x)
dy/dx = (1 / ln(3x)) * (1/x)
dy/dx = log_e(x) / x(ln(3x))
Therefore, the final answer is (c) log_e(x).
Given, y = log_3(x) 3 log_e(x)
Let's solve this step by step.
Step 1: Simplify the given expression.
We know, log_a(b) = log_c(b) / log_c(a)
Applying this formula on the given expression, we get:
y = log_3(x) 3 log_e(x)
y = log_e(x) / log_e(3) 3 log_e(x)
y = (1 / log_e(3)) * log_e(x) log_e(x^3)
y = (1 / ln(3)) * ln(x) 3 ln(x)
y = [(1 / ln(3)) + 3] * ln(x)
Step 2: Differentiate both sides with respect to x.
We get,
dy/dx = [(1 / ln(3)) + 3] * d/dx(ln(x))
dy/dx = [(1 / ln(3)) + 3] * (1/x)
Step 3: Simplify the expression.
dy/dx = [(1 / ln(3)) + 3] * (1/x)
dy/dx = (1 / ln(3x)) * (1/x)
dy/dx = log_e(x) / x(ln(3x))
Therefore, the final answer is (c) log_e(x).
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If y = log_3(x) 3 logex, then dy/dx is :?
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If y = log_3(x) 3 logex, then dy/dx is :? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y = log_3(x) 3 logex, then dy/dx is :? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y = log_3(x) 3 logex, then dy/dx is :?.
If y = log_3(x) 3 logex, then dy/dx is :? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If y = log_3(x) 3 logex, then dy/dx is :? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If y = log_3(x) 3 logex, then dy/dx is :?.
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