-3x
2 = 1/4
(2 raised to the power -3x = 1/4)
well, 2^-2 = 1/4, so
-3x = -2
2 ^ ( - 3 x ) = 1 / 2 ^ ( 3 x ) = 1 / 4 so:
2 ^ ( - 3 x ) = 1 / 4
1 / 2 ^ ( 3 x ) = 1 / 4
Take reciprocials of both sides:
2 ^ ( 3 x ) = 4
2 ^ ( 3 x ) = 2 ^ 2
Take the logarithm base 2 of both sides
3 x = 2 Divide both sides by 3
x = 2 / 3
To solve the equation (2 raised to the power -3x = 1/4), we need to isolate the variable x.
Step 1: Take the logarithm of both sides with base 2.
log2(2 raised to the power -3x) = log2(1/4)
Step 2: Use the logarithmic property to bring down the exponent.
-3x * log2(2) = log2(1/4)
Step 3: Simplify.
-3x * 1 = log2(1/4)
Step 4: Evaluate log2(1/4).
The logarithm with base 2 of 1/4 is -2. Therefore, the equation becomes:
-3x = -2
Step 5: Solve for x.
Divide both sides of the equation by -3:
x = (-2) / (-3)
Step 6: Simplify the expression.
x = 2/3
So the solution to the equation is x = 2/3.