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(1/2x)+1+log6 base5=log(5^(1/x)+125) find x |
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Answer» Given : (1/2x) + 1 + log₅6 = log₅(5¹/ˣ + 125) To find : x Solution: (1/2x) + 1 + log₅6 = log₅(5¹/ˣ + 125) => (1/2x) + 1 = log₅(5¹/ˣ + 125) - log₅6 => (2x + 1) /2x = log₅ ( (5¹/ˣ + 125)/6) => (5¹/ˣ + 125)/6 = 5⁽²ˣ⁺¹⁾/²ˣ => (5¹/ˣ + 125) = 6 * 5⁽²ˣ⁺¹⁾/²ˣ => 5¹/ˣ + 5³ = 5* 5⁽²ˣ⁺¹⁾/²ˣ + 5⁽²ˣ⁺¹⁾/²ˣ => 5¹/ˣ + 5³ = 5⁽⁴ˣ⁺¹⁾/²ˣ + 5⁽²ˣ⁺¹⁾/²ˣ 5¹/ˣ = 5⁽⁴ˣ⁺¹⁾/²ˣ & 5³ = 5⁽²ˣ⁺¹⁾/²ˣ or 5¹/ˣ = 5⁽²ˣ⁺¹⁾/²ˣ & 5³ = 5⁽⁴ˣ⁺¹⁾/²ˣ Case 1 : 5¹/ˣ = 5⁽⁴ˣ⁺¹⁾/²ˣ & 5³ = 5⁽²ˣ⁺¹⁾/²ˣ => 1/x = (4x + 1)/2x => 4x + 1 = 2 => x = 1/4 3 = (2x + 1)/2x => 6x = 2x + 1 => x = x = 1/4 Hence x = 1/4 Case 2 : 5¹/ˣ = 5⁽²ˣ⁺¹⁾/²ˣ & 5³ = 5⁽⁴ˣ⁺¹⁾/²ˣ => 1/x = (2x + 1)/2x => 2x + 1 = 2 => x = 1/2 3 = (4x + 1)/2x => 6x = 4x + 1 => x = 1/2 Hence x = 1/2 x = 1/4 & 1/2 are the Solution Learn More: SOLVE log base 2x-1 of ( x^4+2)/(2x+1) = 1 (Log(base 2) 10).(log(base2) 80)-(log(base2) 5).(log(base2) 160) |
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