Advertisements
Advertisements
Question
Find x.
`(2/5)^(2x + 6) xx (2/5)^3 = (2/5)^(x + 2)`
Advertisements
Solution
We have, `(2/5)^(2x + 6) xx (2/5)^3 = (2/5)^(x + 2)`
Using law of exponents,
am × an = (a)m + n ...[∵ a is non-zero integer]
Then, `(2/5)^(2x + 6 + 3) = (2/5)^(x + 2)`
On comparing powers of `(2/5)`, we get
2x + 6 + 3 = x + 2
⇒ 2x + 9 = x + 2
⇒ x = –7
APPEARS IN
RELATED QUESTIONS
Simplify and write the answer in the exponential form.
`1/8 xx (3)^(-3)`
The value of `1/4^-2` is ______.
`[(2/13)^-6 ÷ (2/13)^3]^3 xx (2/13)^-9` = ______.
50 = 5
The expontential form for `(-2)^4 xx (5/2)^4` is 54.
Find the value of n.
`(2^n xx 2^6)/2^-3 = 2^18`
An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at `1/2` after one hop, `3/4` after two hops, and so on.
- Make a table showing the insect’s location for the first 10 hops.
- Where will the insect be after n hops?
- Will the insect ever get to 1? Explain.
An insect is on the 0 point of a number line, hopping towards 1. She covers half the distance from her current location to 1 with each hop. So, she will be at `1/2` after one hop, `3/4` after two hops, and so on.
Will the insect ever get to 1? Explain.
Find a single machine that will do the same job as the given hook-up.
a (× 24) machine followed by `(xx (1/2)^2)` machine.
If possible, find a hook-up of prime base number machine that will do the same work as the given stretching machine. Do not use (× 1) machines.
