6 x − 28 × 6 − x = 3

Resolved: "6 x − 28 × 6 − x..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Darryl English

Answered question

2022-07-25

6^{x} - 28 \times 6^{- x} = 3

Answer & Explanation

jbacapzh

Beginner2022-07-26Added 18 answers

Let 6^x = y. Then, we have y-28/y = 3. On multiplying both the sides by y, we get y^2-28=3y or, y^2- 3y -28 =0 or, y^2- 7y+4y -28 = 0 or, y(y-7)+4(y-y) = 0 or, (y-7)(y+4) = 0. Hence, either y = 7 or y = -4. Thus, either 6^x = 7 or, 6^x = -4. Now, if 6^x = 7, then, on taking logarithm of both the sides, we have x log 6 = log 7, so that x = log 7/log6. Similarly, if 6^x = -4, then on taking logarithm of both the sides, we have x log 6 = log (-4), so that x = log 7/log(-4). Now, since the logarithm of a negative real number is undefined, the only real solution is x = log 7/log6.

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