Find x: 2 power x+ 2 power x+ 2 power x =192
Answers
Answer:
Step-by-step explanation:
In this expression, factor out 2^x on LHS. Therefore the expression changes to :- 2^x(1+1+1) = 192.
Further, 3.2^x = 192.
=> 2^x = 64
=> x = 6
For easier calculations, I would recommend to memorize certain values till the 10th power of 2 which would help in these kind of problems. I have stated down here for reference.
2^1 = 2
2^2 =4
2^3=8
2^4=16
2^5 =32
2^6= 64
2^7=128
2^8=256
2^9=512
2^10=1024
Step-by-step explanation:
2^x + 2^x + 2^x = 192
We see same terms in addition, As we know repeated addition can be written as Multiplication. So, We express this as product.
2^x is added three times, So it will be 3 * 2^x which is written in the next step.
=> 3(2^x) =192
3 which is in the product when transferred to other side, goes to denominator
=> 2^ x = 192/3
Since 192/3 equals 64, Hence the next step will be
=> 2^x =64
64 = 2 * 2 * 2 * 2 * 2 * 2 , So it can be written as 2^6. Hence the next step is
=> 2^x = 2^6
By laws of exponents, If a^m = a^n, then m = n.
Hence, We get x=6 ( Final answer)
hey mate hope it helps you