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Question
If `log_5((x^4 + y^4)/(x^4 - y^4)) = 2, "show that""dy"/"dx" = (12x^3)/(13y^3)`.
Solution
`log_5((x^4 + y^4)/(x^4 - y^4))` = 2
`(x^4 + y^4)/(x^4 - y^4)` = 52
`(x^4 + y^4)/(x^4 - y^4)` = 25
`(x^4 + y^4)/(x^4 - y^4)` = 25
x4 + y4 = 25(x4 – y)4
x4 + y4 = 25x4 – 25y4
∴ y4 + 25y4 = 25x4 − x4
26y4 = 24x4
Differentiating both sides w.r.t.x, we get
`26d/dxy^4 = 24"d"/"dx"x^4`
`26. 4y^3 dy/dx = 24. 4x^3 d/dx x`
`26y^3 dy/dx = 24x^3`
`dy/dx = (24x^3)/(26y^3)`
`dy/dx = (12x^3)/(13y^3)`
Notes
The question is modified.
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