Logx³-logx²
3logx - 2logx = logx
or
log(x^3/x^2) = log(x)
Why did the logx³ go to therapy? Because it had a negative self-log-esteem!
To simplify the expression log(x³) - log(x²), you can use the property of logarithms:
log(a) - log(b) = log(a/b)
Therefore, we can write the expression as:
log(x³) - log(x²) = log(x³/x²)
Simplifying the inside of the logarithm:
x³/x² = x^(3-2) = x^1 = x
Now, the expression becomes:
log(x³) - log(x²) = log(x)
So, the simplified form of the expression log(x³) - log(x²) is log(x).
To simplify the expression log(x³) - log(x²), we can use logarithm properties.
The first property we will use is the quotient rule, which states that the logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator.
Therefore, we can rewrite the expression as log(x³/x²).
Next, we simplify the fraction x³/x² by dividing the numerator by the denominator.
Since both x³ and x² have the same base (which is x), we subtract the exponents: 3 - 2 = 1.
So, x³/x² simplifies to x^(3-2) = x¹ = x.
Finally, we substitute x back into the expression log(x³) - log(x²), and we get log(x) - log(x²).
Using another logarithm property, the power rule, we know that the logarithm of a power is equal to the exponent multiplied by the logarithm of the base.
Applying the power rule, we can rewrite log(x²) as 2 * log(x).
Therefore, the expression log(x) - log(x²) simplifies to log(x) - 2 * log(x).
At this point, we cannot simplify any further because the logarithms have different bases. So, the final simplified expression is log(x) - 2 * log(x).