Let's simplify the equation step by step:
4^x+1 can be rewritten as 44^x because x+1 = x4^So the equation becomes44^x - 24^x-2 = 124
Now, we can factor out 4^x from both terms4^x(4 - 2*4^-2) = 124
Next, simplify the term inside the parentheses4^x(4 - 2/16) = 124^x(4 - 1/8) = 124^x(32/8 - 1/8) = 124^x(31/8) = 124
Finally, divide both sides by 31/84^x = 124 / (31/84^x = 124 * (8/314^x = 32
To solve for x, we need to find the exponent that 4 needs to be raised to in order to equal 32x = log4(32x = 5/2
Therefore, the value of x is 5/2.
Let's simplify the equation step by step:
4^x+1 can be rewritten as 44^x because x+1 = x4^
So the equation becomes
44^x - 24^x-2 = 124
Now, we can factor out 4^x from both terms
4^x(4 - 2*4^-2) = 124
Next, simplify the term inside the parentheses
4^x(4 - 2/16) = 12
4^x(4 - 1/8) = 12
4^x(32/8 - 1/8) = 12
4^x(31/8) = 124
Finally, divide both sides by 31/8
4^x = 124 / (31/8
4^x = 124 * (8/31
4^x = 32
To solve for x, we need to find the exponent that 4 needs to be raised to in order to equal 32
x = log4(32
x = 5/2
Therefore, the value of x is 5/2.