Advertisements
Advertisements
Question
Find the value of x so that (2–1 + 4–1 + 6–1 + 8–1)x = 1
Solution
We have (2–1 + 4–1 + 6–1 + 8–1)x = 1
Using law of exponents, `a^-m = 1/a^m` ...[∵ a is non-zero integer]
Then, `(1/2 + 1/4 + 1/6 + 1/8)^x = 1`
⇒ `((12 + 6 + 4 + 3)/24)^x = 1` ...[∵ LCM of 2, 4, 6 and 8 = 24]
⇒ `(25/24)^x = 1`
This can be possible only if x = 0. Since, a0 = 1. ....[Law of exponents]
APPEARS IN
RELATED QUESTIONS
The reciprocal of `(2/5)^-1` is ______.
If x be any integer different from zero and m, n be any integers, then (xm)n is equal to ______.
The value of [1–2 + 2–2 + 3–2 ] × 62 is ______.
Find the product of the cube of (–2) and the square of (+4).
Find the value of x so that `(5/3)^-2 xx (5/3)^-14 = (5/3)^(8x)`
By what number should we multiply (–29)0 so that the product becomes (+29)0.
By what number should `((-3)/2)^-3` be divided so that the quotient may be `(4/27)^-2`?
In a repeater machine with 0 as an exponent, the base machine is applied 0 times. What do these machines do to a piece of chalk?
For hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.
Find x.
`((-6)/7)^(x - 7) = 1`
