Maths-
General
Easy

Question

Solve for x∶
8 × 22x + 4 × 2x+1 = 1 + 2x

hintHint:

In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a                   n times.

The correct answer is: Value of x for the given equation is -3.


    Step-by-step solution:-
    8 × 22x + 4 × 2x+1 = 1 + 2x
    ∴ 8 × (2x)2 + 4 × 2x × 21 = 1 + 2x …........................................... (an × am = an+m)
    ∴ 8 × 2x × 2x + 8 × 2x = 1 + 2x …....................................... (x2 = x × x)
    ∴ 8 × 2x (2x + 1) = 1 + 2x .......................................... (Taking 8 × 2x common on LHS)
    ∴ 8 × 2x = 1 ................................................. (Dividing both sides by 2x + 1)
    ∴ 2x = 1/8
    ∴ 2x = 1/23
    ∴ 2x = 2-3 ............................................ (b-n = 1/bn)
    ∴ x = -3 .............................................. (Exponents of the same base in an equation are equal)
    Final Answer:-
    ∴ Value of x for the given equation is -3.

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