4^x - 4^x-1 =24?

Question

4 to the power x minus 4 to the power x-1 equal to 24.

X=?

Answer 1

x=2.5

(4^2.5)-(4^2.5-1)=(4^2.5)-(4^1.5)=24

Answer 2

4^x - 4^x-1 =24

4^x-1 (4-1) = 24

4^x-1 *3 = 24

4^x-1 = 24/3


4^x-1 = 8

2^2(x-2) = 2^3

2x-2 = 3

2x = 5

x = 2.5

Answer 3

4^x - 4^(x-1) = 24

Take note that 4^(x-1) = 4^x times 4^(-1)
And since 4^(-1) = 1/4......

4^x - (1/4) 4^x = 24

(3/4) 4^x = 24

4^x = 24 (4/3) = 32

Since 4 = 2^2 and 32 = 2^5

2^(2x) = 2^5

Hence
2x = 5

x = 2.5 ANS

Hope this helps

Answer 4

4^x - 4^(x - 1) = 24

Factor out 4^x
4^x (1 - 4^-1) = 24

Simplify
4^x = 24/(3/4)

Simplify
4^x = 8 · 4

Thus,
4^x = 32

Make them powers of 2
2^2x = 2^5

Equate the exponents
2x = 5

Thus,
x = 5/2 = 2.5

^_^

Answer 5

4^x - 4^(x-1) = 24
Now 4^(x-1) = 4^x.4^1= 4^x/4
So 4^x - 4^(x-1) = 4^x - 4^x/4
= 3.4^x/4 = 24
Thus 4^x = 24*4/3
= 32

4^x = (2²)^x = 2^(2x) = 32 = 2^5

ie 2x = 5 Thus x = 5/2 (=2.5)

Check

4^(5/2) - 4^(5/2 -1) = 2^5 - 2^3 = 32 - 8 = 24

Answer 6

Notice that 4^x = 4^(x-1) * 4. Factor 4^(x-1) out of both terms on the left hand side, and you're well on your way.

For the rest, it will help to notice that 4 = 2^2.

Answer 7

4^x - 4^x-1 =24

4^x-1 (4-1) = 24

4^x-1 = 8

2^2x-2 = 2^3

2x-2 = 3

2x = 5

x = 2.5

Answer 8

The answer is dude 2.5

Answer 9

x = 2.5

I solved it with intuition. What if the answer had not been so neat? I'd probably rewrite it as

f(x) = A^x - B^(x-Q) - C = 0

And then use Newton's method or Danby's method to find the roots.

g(x) = exp(A) A^x - exp(B) B^(x-Q)
repeat until x converges:
x(i+1) = x(i) - f(x)/g(x)

That's an iterative method, though. Not an analytic one.

Answer 10

2.5

Answer 11

2.5