Question

IF (1.3)^p = (0.13)^q = 10^7.
Find 1/p - 1/q​

Answer 1

Answer:

1/7

Step-by-step explanation:

(1.3)^p=10^7

can also be written as

(13/10)^p=10^7

=> {(13/10)^p}^(1/p)=(10^7)^(1/p)

=> 13/10=10^(7/p). ....1

And for (0.13)^q=10^7

(13/100)^q=10^7

=> {(13/100)^q}^(1/q)=(10^7)^(1/q)

=> 13/100=10^(7/q)

=> 13/10=10^((7/q)+1). ....2

Using 1 and 2, we get

=> 10^((7/q)+1) = 10^(7/p)

=>. (7/q)+1 = 7/p

transposing (7/q)

=>. 1= (7/p) - (7/q)

=>. 1= 7{(1/p)-(1/q)}

=>. 1/7 = (1/p)-(1/q)