Question

solve log¹⁰(x-2)+log¹⁰(x+2)=log¹⁰ 5​

Answer 1

Answer:

Step-by-step explanation:

log a+logb= logab

log (x-2)(x+2)= log 5

x^2-4= 5

x^2=9

x=+-3

it cannot be -3 as log of negative number is not defined

hence answer is 3

Answer 2

Step-by-step explanation:

Given :-

log¹⁰(x-2)+log¹⁰(x+2)=log¹⁰ 5

To find :-

Solve the given equation ?

Solution :-

Given that

log¹⁰(x-2)+log¹⁰(x+2)=log¹⁰ 5

We know that

log ab = log a + log b

=> log¹⁰ (x-2)(x+2) = log¹⁰ 5

=> log¹⁰ (x²-2²) = log¹⁰ 5

Since (a+b)(a-b) = a²-b²

=> log¹⁰ (x²-4) = log¹⁰ 5

=> x²-4 = 5

=> x² = 5+4

=> x² = 9

=> x = ± √9

=> x = ±3

Therefore, x = 3 or -3

But By the definition of logarithms

a = 3

Answer:-

The solution for the given problem is 3

Used formulae:-

→ log ab = log a + log b

→ (a+b)(a-b) = a²-b²

Note :-In log¹⁰ (x-2)+log¹⁰(x+2)=log¹⁰ 5, the base is 10

→ If a > 0, a≠1 and N is a positive number then a^x = N => log N to the base a = x