If 5^{3x - 1} ÷ 25 = 125, find the value of x.

Solution:

Given, the expression is 5^{3x - 1} ÷ 25 = 125.

We have to find the value of x.

We know, 25 = 5²

Also, 125 = 5³

5^{3x - 1} ÷ 25 = 125 can be written as 5^{3x - 1} ÷ 5² = 5³.

Now, 5^{3x - 1} × (1/5²) = 5³

5^{3x - 1} = 5³ × 5²

Considering 5³ × 5²,

a^m × aⁿ = a^{m + n}

Here, a = 5

m = 3

n = 2

So, m + n = 3 + 2

= 5

So, 5³ × 5² = 5⁵

Now, 5^{3x - 1} = 5⁵

So, 3x - 1 = 5

3x = 5 + 1

3x = 6

x = 6/3

x = 2

Therefore, the value of x is 2.

✦ Try This: If 6^{3x - 1} ÷ 36 = 216, find the value of x.

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

NCERT Exemplar Class 8 Maths Chapter 8 Problem 105

Summary:

If 5^{3x - 1} ÷ 25 = 125, the value of x is 2 using the law of exponents a^m × aⁿ = a^{m + n}

☛ Related Questions:

Math worksheets and
visual curriculum

If 53x - 1 ÷ 25 = 125, find the value of x.