solve log2(x+1)-log2x=2
log2 [(x+1)/x ] = 2
(x+1)/x = 2^2 = 4
x+1 = 4 x
x = 1/3
sorry i meant
log2(2x+1)-log2x=2
LOL, well do that the same way.
is x 1/6
(2x+1)/x = 4
2 x + 1 = 4x
2 x = 1
x = 1/2
To solve the equation log2(x+1) - log2x = 2, we can use logarithmic properties and algebraic techniques. Let's break down the steps:
Step 1: Simplify the equation using logarithmic properties.
Using the quotient rule for logarithms, we can rewrite the equation as a single logarithm:
log2((x+1)/x) = 2
Step 2: Convert the logarithmic equation into exponential form.
Recall that for any base a, loga(b) = c can be rewritten as a^c = b.
Applying this concept to our equation, we have:
2^2 = (x+1)/x
Step 3: Simplify the exponential equation.
4 = (x+1)/x
Step 4: Solve for x.
To eliminate the fraction, we can multiply both sides of the equation by x:
4x = x + 1
Step 5: Continue simplifying and solving for x.
Combine like terms by subtracting x from both sides:
4x - x = 1
3x = 1
Finally, divide both sides of the equation by 3 to solve for x:
x = 1/3
Thus, the solution to the equation log2(x+1) - log2x = 2 is x = 1/3.