Question

5²(x+¹) × 5(x+¹) =0.04
find the value of x ​

Answer 1

The value of x is approximately -1 ± 0.0179.

Explanation:

To find the value of x in the equation 5²(x+¹) × 5(x+¹) = 0.04, let’s simplify the equation step by step:

5²(x+¹) × 5(x+¹) = 0.04

25(x+¹) × 5(x+¹) = 0.04

125(x+¹)² = 0.04

Now, let’s solve for (x+¹)²:

125(x+¹)² = 0.04

(x+¹)² = 0.04 / 125

(x+¹)² = 0.00032

To find the value of x, we need to take the square root of both sides:

√((x+¹)²) = √(0.00032)

x + 1 = ±√(0.00032)

Simplifying further:

x + 1 = ±0.0178885438...

Subtracting 1 from both sides:

x = -1 ± 0.0178885438...

Therefore, the value of x is approximately -1 ± 0.0179.

Answer 2

x = -5/3

Explanation:

You want the value of x that satisfies the equation ...

5^(2(x+1))·5^(x+1) = 0.04

Exponents

The rules of exponents tell us ...

(a^b)(a^c) = a^(b+c)

Applying this to the given equation, we have ...

5^(2(x+1))·5^(x+1) = 0.04

5^(2(x+1) +(x+1)) = 5^-2

Equating exponents gives ...

2(x +1) +(x +1) = -2

3x +3 = -2 . . . . . . . . . simplify

3x = -5 . . . . . . . . . . subtract 3

x = -5/3 . . . . . . . . divide by 3

<95141404393>