Question

4^x+1 - 2*4^x-2 = 124

Answer 1

$4*4^x-2*0,0625*4^x=124$

3,875*4^x=124

4^x=32

$2^{2x}=2^5$

x=2,5

Answer 2

Смотри.......................

Answer 3

To solve the equation 4^x+1 - 2*4^x-2 = 124, let's first make some simplifications and rearrange the terms:

1. Express 4^x+1 and 4^x-2 in terms of 4^x: 4^x+1 = 4 * 4^x 4^x-2 = (1/16) * 4^x

Now, substitute these expressions back into the equation:

4 * 4^x - 2 * (1/16) * 4^x = 124

Next, combine the terms with 4^x:

4 * 4^x - (1/8) * 4^x = 124

Now, find a common denominator for the terms:

(32/8) * 4^x - (1/8) * 4^x = 124

Combine the terms with 4^x again:

(32/8 - 1/8) * 4^x = 124

Simplify the coefficient:

(31/8) * 4^x = 124

Now, isolate 4^x by dividing both sides by (31/8):

4^x = 124 / (31/8)

To simplify further, divide the numerator by the denominator:

4^x = 124 * (8/31)

Now, calculate the value on the right-hand side:

4^x = 992 / 31

To find the value of x, take the logarithm of both sides. You can use either the natural logarithm (ln) or the logarithm to the base 4. Let's use the natural logarithm:

ln(4^x) = ln(992 / 31)

Using the property of logarithms, bring down the exponent:

x * ln(4) = ln(992 / 31)

Now, divide both sides by ln(4) to solve for x:

x = ln(992 / 31) / ln(4)

Use a calculator to find the approximate value of x:

x ≈ 3.6767

So, the solution to the equation is approximately x = 3.6767.