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
If x be any non-zero integer and m, n be negative integers, then xm × xn is equal to ______.
(–5)–2 × (–5)–3 = (–5)–6
Solve the following:
`(1/2)^-2 ÷ (1/2)^-3`
`(16 xx 10^2 xx 64)/(2^4 xx 4^2)`
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.
Will the insect ever get to 1? Explain.
Find a single repeater machine that will do the same work as hook-up.
The left column of the chart lists the lengths of input chains of gold. Repeater machines are listed across the top. The other entries are the outputs you get when you send the input chain from that row through the repeater machine from that column. Copy and complete the chart.
| Input Length | Repeater Machine | ||
| × 23 | |||
| 40 | 125 | ||
| 2 | |||
| 162 | |||
The diameter of the Sun is 1.4 × 109 m and the diameter of the Earth is 1.2756 × 107 m. Compare their diameters by division.
Find x.
2x + 2x + 2x = 192
