5^x + 5^{x - 1} = 750. Find x.

Solution:

Given, the expression is 5^x + 5^{x - 1} = 750.

We have to find the value of x.

Considering 5^x + 5^{x - 1},

Using the law of exponents,

a⁻ⁿ = 1/aⁿ

5^x + 5^{x - 1} = 5^x + 5^x/5

= 5^x (1 + 1/5)

= 5^x (6/5)

Now, 5^x (6/5) = 750

5^x = 750 × (5/6)

5^x = 125 × 5

5^x = 625

We know, 625 = 5⁴

So, 5^x = 5⁴

On comparing the powers,

x = 4

Therefore, the value of x is 4.

✦ Try This: 6^x + 6^{x - 2} = 660. Find x.

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

NCERT Exemplar Class 8 Maths Chapter 8 Problem 177(6)

5^x + 5^{x - 1} = 750. Find x.

Summary:

5^x + 5^{x - 1} = 750. The value of x is 4 using the law of exponents a⁻ⁿ = 1/aⁿ.

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