4* 4^x/2 =1024
Where do you begin since it is expoential?
Is it 2^2+ 4(^2(^x/2) = 2^10.Then simplifying ?
good strategy
[2^2 *(2^2)^x] / 2 = 2^10
(2^2)^(x + 1) = 2^11
or , assuming you meant : 4* 4^(x/2) =1024
4^(x/2 + 1) = 4^5
x/2 + 1 = 5
x/2 = 4
x = 8
If you meant: 4* (4^x)/2 =1024, the way you typed it
(4^x)/2 = 256
4^x = 512
xlog4 = log512
x = log512/log4 = 4.5
Thank you! Sorry for the confusion of the way I typed it.
To solve the equation 4 * 4^(x/2) = 1024, you first simplify the expression on the left side of the equation by combining the exponents of the base 4.
Since you have 2^2 * 4^(x/2), you can rewrite 4 as 2^2:
2^2 * (2^2)^(x/2) = 1024.
Then, apply the exponent rule which states that (a^m)^n = a^(m*n). In this case, you multiply the exponents:
2^2 * 2^(2*(x/2)) = 1024.
Simplifying further:
2^2 * 2^x = 1024.
Using the exponent rule again, you add the exponents of the base 2:
2^(2 + x) = 1024.
Now, since both sides of the equation have the same base, you can set the exponents equal to each other:
2 + x = 10.
Solving for x, you subtract 2 from both sides:
x = 8.
So, the solution to the equation 4 * 4^(x/2) = 1024 is x = 8.