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1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x?
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Given Equation:
1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9
Step 1: Rewrite the equation using properties of logarithms
log₃√(x + 1) - log₉(1 - x) = log₉(2x³)
Step 2: Use the properties of logarithms to simplify the equation
log₉(√(x + 1) / (1 - x)) = log₉(2x³)
Step 3: Remove the logarithms by converting the equation to exponential form
√(x + 1) / (1 - x) = 2x³
Step 4: Simplify the equation
√(x + 1) = 2x³(1 - x)
(x + 1) = 4x⁶(1 - x)²
x + 1 = 4x⁶(1 - 2x + x²)
x + 1 = 4x⁶ - 8x⁷ + 4x⁸
Step 5: Rearrange the terms and set the equation equal to zero to solve for x
4x⁸ - 8x⁷ - x + 1 = 0
4x⁸ - 8x⁷ - x + 1 = 0
Step 6: Use a numerical method or a graphing calculator to find the approximate solution for x
By solving the equation, we find that x ≈ 0.429
Therefore, the approximate solution for x is 0.429.
1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9
Step 1: Rewrite the equation using properties of logarithms
log₃√(x + 1) - log₉(1 - x) = log₉(2x³)
Step 2: Use the properties of logarithms to simplify the equation
log₉(√(x + 1) / (1 - x)) = log₉(2x³)
Step 3: Remove the logarithms by converting the equation to exponential form
√(x + 1) / (1 - x) = 2x³
Step 4: Simplify the equation
√(x + 1) = 2x³(1 - x)
(x + 1) = 4x⁶(1 - x)²
x + 1 = 4x⁶(1 - 2x + x²)
x + 1 = 4x⁶ - 8x⁷ + 4x⁸
Step 5: Rearrange the terms and set the equation equal to zero to solve for x
4x⁸ - 8x⁷ - x + 1 = 0
4x⁸ - 8x⁷ - x + 1 = 0
Step 6: Use a numerical method or a graphing calculator to find the approximate solution for x
By solving the equation, we find that x ≈ 0.429
Therefore, the approximate solution for x is 0.429.
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1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x?
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1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x?.
1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 1/2 log (x +1) to the base 3 - log (1-x ) to the base 9 = log (2x 3) to the base 9 Find x?.
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