d:[["$","title","0",{"children":"IIM Kozhikode - If y > 0, and _y(x) = 4, _10y (25x) = 2 hold, what is y? | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined We need to find the value of y using the two given logarithmic equations.

Convert the logarithmic equations to exponential form: From _y(x) = 4, we >=t: x = y^4 From _10y(25x) = 2, we >=t: 25x = (10y)^2 = 100y^2

Substitute to eliminate x: Since x = y^4, we can substitute this into our second equation: 25x = 100y^2 25(y^4) = 100y^2 25y^4 = 100y^2

Solve for y: Divide both sides by 25y^2 (since y > 0): 25y^425y^2 = 100y^225y^2 y^2 = 4 Since y > 0, we take the positive square root: y = 2

Verify our answer: If y = 2, then x = y^4 = 2^4 = 16 Check equation 1: _2(16) = _2(2^4) = 4 ✓ Check equation 2: _20(400) = _20(20^2) = 2 ✓ Therefore, y = 2"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"IIM-K (BMSAT),QA,Modern Math,Logarithms"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"IIM Kozhikode - If y > 0, and _y(x) = 4, _10y (25x) = 2 hold, what is y? | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined We need to find the value of y using the two given logarithmic equations.

Convert the logarithmic equations to exponential form: From _y(x) = 4, we >=t: x = y^4 From _10y(25x) = 2, we >=t: 25x = (10y)^2 = 100y^2

Substitute to eliminate x: Since x = y^4, we can substitute this into our second equation: 25x = 100y^2 25(y^4) = 100y^2 25y^4 = 100y^2

Solve for y: Divide both sides by 25y^2 (since y > 0): 25y^425y^2 = 100y^225y^2 y^2 = 4 Since y > 0, we take the positive square root: y = 2

Verify our answer: If y = 2, then x = y^4 = 2^4 = 16 Check equation 1: _2(16) = _2(2^4) = 4 ✓ Check equation 2: _20(400) = _20(20^2) = 2 ✓ Therefore, y = 2"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/iimk-bmsat/2025/QA/18"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | IIM Kozhikode Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"IIM Kozhikode - If y > 0, and _y(x) = 4, _10y (25x) = 2 hold, what is y? | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined We need to find the value of y using the two given logarithmic equations.

Convert the logarithmic equations to exponential form: From _y(x) = 4, we >=t: x = y^4 From _10y(25x) = 2, we >=t: 25x = (10y)^2 = 100y^2

Substitute to eliminate x: Since x = y^4, we can substitute this into our second equation: 25x = 100y^2 25(y^4) = 100y^2 25y^4 = 100y^2

Solve for y: Divide both sides by 25y^2 (since y > 0): 25y^425y^2 = 100y^225y^2 y^2 = 4 Since y > 0, we take the positive square root: y = 2

Verify our answer: If y = 2, then x = y^4 = 2^4 = 16 Check equation 1: _2(16) = _2(2^4) = 4 ✓ Check equation 2: _20(400) = _20(20^2) = 2 ✓ Therefore, y = 2"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20"]

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