Advertisements
Advertisements
Question
Find x.
23x = 82x + 1
Solution
We have, 23x = 82x + 1
⇒ 23x = (23)2x + 1
⇒ 23x = (2)6x + 3 ...[∵ (am)n = (a)m × n]
On comparing the power of 2, we get
3x = 6x + 3
⇒ –3 = 3x
⇒ x = –1
APPEARS IN
RELATED QUESTIONS
The value of (7–1 – 8–1) –1 – (3–1 – 4–1) –1 is ______.
The value of `1/4^-2` is equal to 16.
Planet A is at a distance of 9.35 × 106 km from Earth and planet B is 6.27 × 107 km from Earth. Which planet is nearer to Earth?
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.
Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression 3–t. What fraction of substance remains after 7 half-lives?
Fill in the blanks
Find a single machine that will do the same job as the given hook-up.
a (× 599) machine followed by a (5–100) 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.
Find a repeater machine that will do the same work as a `(xx 1/8)` machine.
Mass of Mars is 6.42 × 1029 kg and mass of the Sun is 1.99 × 1030 kg. What is the total mass?