Solve:
logx^3 - log2 = log(2x^2)
logx^3 - log2 = log(2x^2)
logx^3 - log(2x^2) = log2
log(x^3/(2x^2)) = log2
log(x/2) = log2
x/2 = 2
x = 4
Log x³ - log 2 = log (2x²)
Log x³ - log 2 = log (2×x²)
Log x³ - log 2 = log 2 + log x²
Log x³ - log x² = log 2 + log 2
Log (x³/x²) = log (2×2)
x^3-2 = 4
x=4
To solve the equation log(x^3) - log(2) = log(2x^2), we can use the properties of logarithms. The equation involves subtraction and addition of logarithms, which can be converted into multiplication and division.
First, let's apply the quotient rule of logarithms. According to the quotient rule, log(a) - log(b) = log(a/b).
Using this rule, we can rewrite the equation as:
log(x^3/2) = log(2x^2)
Since the logarithms on both sides of the equation are equal, we can remove the logarithms:
x^3/2 = 2x^2
Next, let's simplify the equation further:
Multiply both sides of the equation by 2 to eliminate the fraction:
2 * (x^3/2) = 2 * 2x^2
This simplifies to:
x^3 = 4x^2
Now, we can rearrange the equation to bring all terms to one side:
x^3 - 4x^2 = 0
Factoring out an x^2:
x^2 (x - 4) = 0
Now we have two possible solutions for x:
1. x^2 = 0
This implies x = 0.
2. (x - 4) = 0
Solving for x gives x = 4.
Therefore, the equation log(x^3) - log(2) = log(2x^2) is satisfied when x = 0 or x = 4.
To solve the equation log(x^3) - log(2) = log(2x^2), we can use the properties of logarithms.
First, let's use the property of logarithms that states that log(a) - log(b) = log(a/b). Applying this to the equation, we get:
log(x^3/2) = log(2x^2)
Now, we can eliminate the logarithms by equating the expressions inside the logarithms:
x^3/2 = 2x^2
To solve for x, we can simplify the equation further:
x^3/2 - 2x^2 = 0
To solve this equation, we can factor out an x^2 term:
x^2(x/2 - 2) = 0
Now, we have two factors: x^2 = 0 and (x/2 - 2) = 0.
For x^2 = 0, the only solution is x = 0.
For (x/2 - 2) = 0, we can solve for x:
x/2 - 2 = 0
x/2 = 2
x = 4
Therefore, the two solutions to the equation log(x^3) - log(2) = log(2x^2) are x = 0 and x = 4.