Find the value of x so that (2⁻¹ + 4⁻¹ + 6⁻¹ + 8⁻¹)^x = 1.

Solution:

Given, the expression is (2⁻¹ + 4⁻¹ + 6⁻¹ + 8⁻¹)^x = 1.

We have to find the value of x.

a⁻ⁿ = 1/aⁿ

So, 2⁻¹ = 1/2

Similarly, 4⁻¹ = 1/4

6⁻¹ = 1/6

8⁻¹ = 1/8

LHS: (2⁻¹ + 4⁻¹ + 6⁻¹ + 8⁻¹)^x

= (1/2 + 1/4 + 1/6 + 1/8)^x

= [(12 + 6 + 4 + 3)/24]^x

= (25/25)^x

RHS: 1

So, (25/25)^x = 1

Using law of exponents,

a° = 1, where a ≠ 0

Now, (25/24)^x = 1 when (25/24)⁰

x = 0

Therefore, the value of x is 0.

✦ Try This: Find the value of x so that (1⁻¹ + 2⁻¹ + 3⁻¹ + 5⁻¹)^x = 1.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

NCERT Exemplar Class 8 Maths Chapter 8 Problem 99(iii)

Summary:

The value of x so that (2⁻¹ + 4⁻¹ + 6⁻¹ + 8⁻¹)^x = 1 is 0 using the law of exponents

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Find the value of x so that (2⁻¹ + 4⁻¹ + 6⁻¹ + 8⁻¹)x = 1.