Question

if log¹⁰x=a+b and y=10 power a-b then find the value of log¹⁰(x²y³) in terms of a-b?​ pls ans the question I want immediately?​

Answer 1

Answer:

log¹⁰x=a+b and y=10 power a-b then find the value of log¹⁰(x²y³) in terms of a-b? pls ans the question I want

Answer 2

Step-by-step explanation:

Given :-

log¹⁰x=a+b and y=10 power a-b

To find :-

Find the value of log¹⁰(x²y³) in terms of a-b ?

Solution :-

Given that

log¹⁰x=a+b-------(1)

y=10^(a-b)

=> log ¹⁰ y = a -b -----(2)

Now,

log ¹⁰ (x²y³)

We know that

log ab = log a + log b

=> log ¹⁰ x² + log ¹⁰ y³

We know that

log a^m = m log a

=>2 log ¹⁰x + 3 log¹⁰ y

=> 2 (a+b)+3(a-b)

=> 2a+2b +3a-3b

=> (2a+3a)+(2b-3b)

=> 5a -b

Answer:-

The value of log¹⁰ (x²y³) is 5a -b

Used formulae:-

→ log ab = log a + log b

→ log a^m = m log a